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The Great Telescope of the Lick Observatory. Aperture, 3G inches; Lenglh, 57 feet. 



THE 



Elements of Astronomy 



A TEXT-BOOK 



v\ou 



CHARLES A r . YOUNG, Ph.D. LL.D. 



Professor of Astronomy in the College of New Jersey (Princeton; 

Author of "The Sun," and of a "General Astronomy for 

Colleges and Scientific Schools " 



BE VISED EDITION 
With Synopsis 



Boston, U.S.A., and London 

PUBLISHED BY GrNN & COMPANY 

1897 



K. 






.%«' 



Entered at Stationers' Hall. 



Copyright, 1889 and 1897. 
By CHARLES A. YOUNG. 



All Rights Reseryed. 



Typography by J. S. Cushing & Co., Boston, U.S.A., 



PRES9WORK BY GlNN & Co., BOSTON, U.S.A. 



>(7 



PREFACE. 



The present volume is a new work, and not a mere 
abridgment of the author's "General Astronomy." Much 
of the material of the larger book has naturally been in- 
corporated into this, and many of its illustrations are 
used ; but everything has been worked over with refer- 
ence to the wants of institutions which demand a more 
elementary and less extended course than that presented 
in the " General Astronomy." 

It has not always been easy to decide just how far to 
go in cutting Sown and simplifying. On the one hand 
the students who are expected to use the present book are 
not children, but have presumably mastered the elementary 
subjects which properly precede the study of Astronomy, 
and it is an important part of their remaining educa- 
tion to make them familiar with astronomical terms and 
methods ; on the other hand it is very easy to assume too 
much, and to make the book difficult and incomprehensible 
by the use of too many unfamiliar terms, and the unpre- 
pared presentation of new ideas and demonstrations — and 
the danger is greater in a brief course than in a longer 
one. 

While therefore the writer has tried to treat every sub- 
ject simply and clearly, he has not discarded the use of 
technical terms in proper places, and he has always sought 



IV PREFACE. 

to stimulate thought, to discourage one-sided and narrow 
ways of looking at things, and to awaken the desire for 
further acquisition. 

The book presupposes students anxious to learn, and 
an instructor who understands the subject in hand, 
and the art of teaching. 

Special attention has been paid to making all statements 
correct and accurate as far as they go. Many of them are 
necessarily incomplete, on account of the elementary char- 
acter of the work ; but it is hoped that this incomplete- 
ness has never been allowed to degenerate into untruth, 
and that the pupil will not afterwards have to unlearn 
anything that the book has taught him. 

In the text no mathematics higher than elementary 
algebra and geometry is introduced ; in the foot notes 
and in the appendix an occasional trigonometric formula 
appears. 

Certain subjects, which, while they certainly ought to 
be found within the covers of every text-book of Astron- 
omy, are perhaps not essential to an elementary course, 
have been relegated to an appendix. Where time allows, 
the instructor will find it advisable to include some of 
them at least in the student's work. 

A brief Uranography is also presented, covering the 
constellations visible in the United States, with maps on 
a scale sufficient for the easy identification of all the prin- 
cipal stars. It includes also a list of such telescopic 
objects in each constellation as are easily found and lie 
within the power of a small telescope. 

The author is under special obligations to Messrs. 
Kelley of Haverhill, Lambert of Fall River, and Par- 



PREFACE. V 

menter of Cambridgeport, for valuable suggestions and 
assistance in preparing the work, and to his assistant, Mr. 
Reed, for help in the proof-reading : also to Warner & 
Swasey for the cut of the Lick telescope which forms the 
frontispiece. 

In the present issue all the errata detected in previous 
impressions have been corrected, and a number of "ad- 
denda," embodying recent important observations and 
discoveries, have been prefixed. 



PREFACE TO THE REVISED EDITION OF 1897. 



The progress of Astronomy since the first publication of 
this work has been such as to require a thorough revision and 
partial rewriting of the book in order to make it fairly rep- 
resentative of the existing state of the science. Numerous 
changes and corrections have been made, with some consider- 
able additions ; but the necessary alterations have been so 
managed that it is believed that no serious inconvenience will 
arise in using the old and new editions together. 

A " Synopsis for Review and Examination " has been added 
which, it is hoped, will be found useful by both teachers and 
pupils. 

C. A. Young. 

Princeton, N. J., 
June, 1897. 



CONTENTS. 



PAGES 

INTRODUCTION 1-4 

CHAPTER I. — Fundamental Notions and Definitions: the 

" Doctrine of the Sphere " 5-28 

CHAPTER II. — Fundamental Problems of Practical Astron- 
omy : the Determination of Latitude, of Time, of Longitude, 
of the Place of a Ship at Sea, and of the Position of a Heav- 
enly Body 29-44 

CHAPTER III. — The Earth: its Form, Rotation, and Dimen- 
sions ; Mass, Weight, and Gravitation in General ; the Earth's 
Mass and Density 45-66 

CHAPTER IV. — The Orbital Motion of the Earth and 
its Consequences : Precession ; Aberration ; the Equation of 
Time : the Seasons and the Calendar . . . . . 67-87 

CHAPTER V.— The Moon: her Orbital Motion; her Distance, 
Dimensions, Mass, and Density; Rotation and Librations ; 
Phases; her Light and Heat and Physical Condition; Tele- 
scopic Aspect and Surface Features 88-113 

CHAPTER VI. — The Sun : its Distance, Dimensions, Mass, and 
Density ; its Rotation and Equatorial Acceleration ; Methods 
of Studying its Surface ; Sun Spots, their Nature, Dimensions, 
Development, and Motions ; their Distribution and Perio- 
dicity ; Sun-Spot Theories 114-132 



Vlll CONTENTS. 

CHAPTER VII. — The Spectroscope, the Solar Spectrum, 
and the Chemical Constitution of the Sun : the Sun-Spot 
Spectrum ; Doppler's Principle ; the Chromosphere and 
Prominences ; the Corona ; the Sun's Light ; the Sun's Heat ; 
Theory of its Maintenance and Speculations regarding the 
Age of the Sun . . . 133-160 

CHAPTER VIII. — Eclipses : Form and Dimensions of Shadows; 
Eclipses of the Moon ; Solar Eclipses, Total, Annular, and 
Partial ; Ecliptic Limits, and number of Eclipses in a Year ; 
Recurrence of Eclipses, and the Saros ; Occultations . 161-174 

CHAPTER IX. — Celestial Mechanics : the Laws of Central 
Force ; Circular Motion ; Kepler's Laws ; Newton's Verifica- 
tion of the Theory of Gravitation ; the Conic Sections ; the 
Problem of Two Bodies ; the Problem of Three Bodies and 
Perturbations ; the Tides 175-198 

CHAPTER X. —The Planets in General : Bode's Law ; Ap- 
parent Motions ; the Elements of a Planet's Orbit ; Determi- 
nation of Period and Distance ; Planetary Perturbations and 
Stability of the System ; Determination of the Data relating 
to the Planets themselves ; their Diameters, Masses, Rotations, 
etc. ; Herschel's Illustration of the Scale of the System . 199-219 

CHAPTER XL — The Terrestrial and Minor Planets : Intra- 

Mercurial Planets, and the Zodiacal Light . . . 220-242 

CHAPTER XII. — The Major Planets : Jupiter, its Satellites, 
the Equation of Light, and the Distance of the Sun ; Saturn, 
its Rings and Satellites ; Uranus, its Discovery and Satellite 
System ; Neptune, its Discovery ; its Satellite . . 243-263 

CHAPTER XIII. — Comets and Meteors : Comets, their Num- 
ber, Designation, and Orbits ; their Constituent Parts and 
Appearance ; their Spectra, Physical Constitution, and Proba- 
ble Origin ; Aerolites, their Fall and Characteristics ; Shoot- 
ing Stars and Meteoric Showers ; Connection between Meteors 
and Comets 264-302 



CONTENTS. IX 

CHAPTER XIV. — The Stars : their Nature, Number, and Des- 
ignation ; Star Catalogues and Charts ; their Proper Motions, 
and the Motion of the Sun in Space ; Stellar Parallax ; 
Star Magnitudes and Photometry ; Variable Stars ; Stellar 
Spectra 303-332 

CHAPTER XV. —The Stars (continued): Double and Multiple 
Stars ; Clusters and Nebulae ; the Milky Way, and Distribu- 
tion of Stars In Space ; the Stellar Universe ; Cosmogony and 
the Nebular Hypothesis 333-360 

APPENDIX. 

CHAPTER XVI. — Supplementary to Articles in the Text : 
Celestial Latitude and Longitude. — Corrections to a Meas- 
ured Altitude. — The Local Time from a Single Altitude of 
the Sun. — Determination of Azimuth. — Theory of the Fou- 
cault Pendulum. — Measurement of Mass independent of 
Gravity. — The Equation of Time. — The Spectroscope and 
the Solar Prominences.' — The Equation of Doppler's Prin- 
ciple. — Areal, Linear, and Angular Velocities. — Gravitation 
proved by Kepler's Harmonic Law. — Newton's Verification 
of Gravitation by Means of the Moon. — The Conic Sections. 

— Elements of a Planet's Orbit. — The Mass of a Planet. — 
Danger from Comets. — Twilight 361-382 

CHAPTER XVII. — Determination of Solar and Stellar Par- 
allax : Historical. — Geometrical Methods of finding the 
Parallax of the Sun : Oppositions of Mars ; Transits of 
Venus and Halley's Method ; De 1' Isle's Method ; Helio- 
metric and Photographic Methods ; Gravitational Methods. 

— Absolute and Differential Methods of determining Stellar 
Parallax 383-395 

CHAPTER XVIII. — Astronomical Instruments: The Tele- 
scope, Simple Refracting, Achromatic, and Reflecting. — 
The Equatorial. — The Filar Micrometer and the Heli- 
ometer. — The Transit Instrument. — The Clock and the 
Chronograph. — The Meridian Circle. — The Sextant. — The 
Pyrheliometer 396-426 



X CONTENTS. 

TABLES OF ASTRONOMICAL DATA: 

I. Astronomical Constants 
II. The Principal Elements of the Solar System 

III. The Satellites of the Solar System 

IV. The Principal Variable Stars 

V. The Best Determined Stellar Parallaxes 
VI. Motion of Stars in the Line of Sight 
VII. Orbits of Binary Stars .... 
The Greek Alphabet and Miscellaneous Symbols 



427 
428 
429 
430 
431 
432 
433 
434 



SUGGESTIVE QUESTIONS 435-438 

SYNOPSIS FOR REVIEW AND EXAMINATION . 439-450 

INDEX ...... . . . 451-402 

SUPPLEMENTARY INDEX 463,404 

URANOGRAPHY AND STAR-MAPS .... 465-508 






INTRODUCTION. 



oi^o 



1. The earth is a huge ball about 8000 miles in diameter, 
composed of rock and water, and covered with a thin envelope 
of air and cloud. Whirling as it flies, it rushes through empty 
space, moving with a speed fully fifty times as great as that of 
the swiftest cannon-ball. On its surface we are wholly uncon- 
scious of the motion, because it is perfectly steady and without 
jar. 

As we look off at night we see in all directions the countless 
stars, and conspicuous among them, and looking like stars, 
though very different in their real nature, are scattered a few 
planets. Here and there appear faintly shining clouds of 
light, like the so-called Milky Way and the nebulae, and per- 
haps, now and then, a comet. Most striking of all, if she 
happens to be in the heavens at the time, though really the 
most insignificant of all, is the moon. By day the sun alone 
is visible, flooding the air with its light and hiding the other 
heavenly bodies from the unaided eye, but not all of them 
from the telescope. 

2. The Heavenly Bodies. — The bodies thus seen from the 
earth are known as the u heavenly bodies" For the most part 
they are globes like the earth, whirling on their axes, and mov- 
ing swiftly through space, though at such distances from us 
that their motions can be detected only by careful observation. 

They may be classified as follows: First, the solar system 
proper, composed of the sun, the planets which revolve around 



2 INTRODUCTION. [§ 2 

it, and the satellites, which attend the planets in their motion 
around the sun. The moon thus accompanies the earth, which 
herself belongs among the planets. The distances between 
these bodies are enormous as compared with the size of the 
earth, and the sun which rules them all is a body of almost 
inconceivable magnitude. 

Next, we have the comets and the meteors which, while they 
acknowledge the sun's dominion, move in orbits of a different 
shape from those of the planets, and are bodies of a very 
different character. Finally, we have the stars and nebulce, 
at distances from us immensely greater than even those which 
separate the planets. The stars are suns, bodies comparable 
with our own sun in size and nature, and, like it, self-luminous, 
while the planets and their satellites shine only by reflected 
sunlight. Of the nebulae we know very little, except that they 
are cloud-like masses of self-luminous matter, and belong to 
the region of the stars. 

3. Subject-Matter of Astronomy. — Astronomy is the science 
which treats of the heavenly bodies. It investigates (a) their 
motions and the laws which govern them; (b) their nature, 
dimensions, and characteristics ; (c) the influence they exert 
upon each other either by their attraction, their radiation, or 
in any other way. 

Astronomy is the oldest of the natural sciences : nearly the 
earliest records that we find in the annals of China and upon 
the inscribed " library bricks " of Assyria and Babylon relate 
to astronomical subjects, such as eclipses and the positions of 
the planets. Obviously in the infancy of the race the rising 
and setting of the sun, the progress of the seasons, and the 
phases of the moon must have compelled the attention of even 
the most unobservant. 

As Astronomy is the oldest of the sciences, so also it is one 
of the most perfect, and in certain aspects the noblest, as 
being the most " unselfish," of them all. 



§ 4] INTRODUCTION. 3 

4. Utility. — Although not bearing so directly upon the 
material interests of life as the more modern sciences of Phys- 
ics and Chemistry, it is really of high utility. It is by means 
of Astronomy that the latitudes and longitudes of places upon 
the earth's surface are determined, and by such determinations 
alone is it possible to conduct vessels upon the sea. If we can 
imagine that some morning men should awake with Astronomy 
forgotten, all almanacs and astronomical tables destroyed, and 
sextants and chronometers demolished, commerce would prac- 
tically cease, and so far as intercourse by navigation is con- 
cerned, the world would be set back to the days before Columbus. 
Moreover, all the operations of surveying upon a large scale, such 
as the determination of the boundaries of countries, depend 
more or less upon astronomical observations. The same is true 
of all operations which, like the railway service, require an ac- 
curate knowledge and observance of the time ; for the funda- 
mental time-keeper is the diurnal revolution of the heavens, 
as determined by the astronomer's transit-instrument. 

In ancient times the science was supposed to have a still higher 
utility. It was believed that human affairs of every kind, the welfare 
of nations, and the life history of individuals alike, were controlled, 
or at least prefigured, by the motions of the stars and planets ; so 
that from the study of the heavens it ought to be possible to predict 
futurity. The pseudo-science of Astrology based upon this belief 
really supplied the motives that led to most of the astronomical obser- 
vations of the ancients. Just as modern Chemistry had its origin in 
Alchemy, so Astrology was the progenitor of Astronomy. 

5. Place in Education. — Apart from the utility of Astron- 
omy in the ordinary sense of the word, the study of the 
science is of the highest value as an intellectual training. 
No other science so operates to give us on the one hand just 
views of our real insignificance in the universe of space, mat- 
ter, and time, or to teach us on the other hand the dignity 
of the human intellect as the offspring, and measurably the 



4 INTRODUCTION, [§ 5 

counterpart, of the Divine; able in a sense to "comprehend" 
the universe, and know its plan and meaning. The study of 
the science cultivates nearly every faculty of the mind; the 
memory, the reasoning power, and the imagination all receive 
from it special exercise and development. By the precise 
and mathematical character of many of its discussions it en- 
forces exactness of thought and expression, and corrects that 
vague indefiniteness which is apt to be the result of pure lit- 
erary training. On the other hand, by the beauty and gran- 
deur of the subjects it presents, it stimulates the imagination 
and gratifies the poetic sense. In every way it well deserves 
the place which has long been assigned to it in education. 

6. The present volume does not aim to make finished 
astronomers of high-school pupils. That would require years 
of application, based upon a thorough mathematical training 
as a preliminary. Our little book aims only to present such a 
view of the elements of the science as will give the pupils of 
our high schools an intelligent understanding of its leading 
facts, — not a mere parrot-like knowledge of them, but an 
understanding both of the facts themselves and of the general 
methods by which we ascertain them. These are easily mas- 
tered by a little attention, and that without any greater degree 
of mathematical knowledge than may confidently be expected 
of pupils in the latter years of a high-school course. Nothing 
but the simplest Arithmetic, Algebra, and Geometry will be 
required to enable one to deal with anything in the book, 
except that now and then a trigonometric equation may be 
given in a note or in the Appendix for the benefit of those 
who understand that branch of mathematics. 

The occasional references to "Physics " refer to Gage's Principles of 
Physics, and those to "Gen. Ast." relate to the author's General 
Astronomy, or College Text-Book. 



S 7] T H E C E LEST I A L S 1 ' H E II E, 



CHAPTER I. 

FUNDAMENTAL NOTIONS AND DEFINITIONS, AND THE 
DOCTRINE OF THE SPHERE. 

7. The Celestial Sphere. — The sky appears as a hollow 
vault, to which the stars seem to be attached, like specks of 
gilding upon the inner surface of a dome. We cannot judge 
of the distance of the concavity from the eye, further than 
to perceive that it must be very far away, because it lies be- 
yond even the remotest terrestrial objects. It is therefore nat- 
ural, and it is extremely convenient from a mathematical point 
of view, to regard the distance of the heavens as unlimited. 
The celestial sphere, as it is called, is conceived of as so enor- 
mous that the whole material universe lies in its centre like a 
few grains of sand in the middle of the dome of the Capitol. 
The imaginary radius of the celestial sphere is assumed to be 
immeasurably greater than any actual distance known, and 
greater than any quantity assignable, — in technical language, 
m ath em a tically infinite. 

There are other ways of regarding the celestial sphere, which are 
equally correct and lead to the same general results without requiring 
the assumption of an infinite radius, but on the whole they are more 
complicated and less convenient than the one above indicated, which 
is that usually accepted among astronomers. 

8. Vanishing Point. — Since the radius of the celestial 
sphere is thus infinite, any set of lines which are parallel to 
each other, if extended indefinitely, will appear to pierce it at 
a single point. The real distances of the parallel lines from 



PLACE OF A HEAVENLY BODY. 



[§8 



each other remain, of course, unchanged however far they may 
be produced ; so that whatever may be the radius of the 
sphere, they actually pierce the surface in a group of separate 
points. But since the radius of the sphere is " infinite/ 7 the 
apparent size of the group of points, as seen from the earth, 
will be less than any assignable quantity. In other words, to 
the eye the area occupied by the group on the surface of the 
sphere will shrink to a mere point, — the " vanishing point n of 
perspective. Thus the axis of the earth, and all lines parallel 
to it, pierce the heavens at the celestial pole; and the plane 
of the earth's equator, which keeps parallel to itself during 
her annual circuit around the sun, marks out only one celestial 
equator in the sky. 

9. Place of a Heavenly Body. — This is simply the point 
where a line, drawn from the observer through the body in 
question and continued onward, pierces the sphere. It de- 
pends solely upon the direction 
of the body, and is obviously 
in no way affected by its dis- 
tance. Thus in Fig. 1, A, B, C, 
etc., are the apparent places of 
a, &, c, the observer being at 0. 
Objects that are nearly in line 
with each other, as h, /, A', will 
appear close together in the sky, 
however great their real dis- 
tance from each other may be. 
The moon, for instance, often 
looks to us "very near 7 ' a star, 

which is really of course at an immeasurable distance beyond 
her. 

10. Angular Measurement. — It is clear that we cannot prop- 
erly measure the apparent distance of two heavenly bodies 
from each other in the sky by feet or inches. To say that two 




Fig. 1. 



§ 10] ANGTJLAK MEASUREMENT. 7 

stars are about five feet apart, for instance (and it is not very 
uncommon to hear such an expression), means nothing unless 
you tell how far from the eye the five-foot measure is to be 
held. If 20 feet away, it means one thing, and corresponds, 
nearly, to the apparent length of the " Dipper-handle " in the 
sky (see Art. 23) ; if 100 feet away, it corresponds to an 
apparent distance only about one-fifth as great, or to one of 
the shorter sides of the " Dipper-bowl " (see Art. 23) ; but if 
the five-foot measure were a mile away, its length would cor- 
respond to an apparent distance about one-tenth the apparent 
diameter of the moon. The proper units for expressing appar- 
ent distances in the sky are those of angle, viz. : radians, or else 
degrees (°), minutes ('), and seconds ("). The Great Bear's 
tail or Dipper-handle is about 16 degrees long, the long side of 
the Dipper-bowl is about 10 degrees, the shorter sides are 4° or 
5° ; the moon is about half a degree, or 30', in diameter. 

11. The student will remember that a degree is one three-hundred- 
ancl-sixtieth of the circumference of a circle, so that a quarter of the 
circumference, or the distance from the point overhead to the horizon, 
is 90°; also, that a minute is the sixtieth part of a degree, and a sec- 
ond the sixtieth part of a minute. The radian is the angle measured 

360° 

by an arc of the circumference equal to its radius. It is , or 

'2tt 
(approximately) 57°.3, 3137'. 7, or 206261". 8. 

It is very important, also, that the student in Astronomy as soon as 
possible should accustom himself to estimate celestial measures in 
these angular units. A little practice soon makes it easy, though at 
first one is apt to be embarrassed by the fact that the sky looks to the 
eye not like a true hemisphere, but a flattened vault, so that all esti- 
mates of angular distances for objects near the horizon are apt to be 
exaggerated. The moon when rising or setting looks to most per- 
sons much larger 1 than when overhead, and the " Dipper-bowl " 



1 This is due to the fact that when a heavenly body is overhead there 
are no intervening objects by which we can estimate its distance from us, 
while at the horizon we have the whole landscape between us and it. This 



8 DISTANCE AND APPABEMT SIZE. [§ 12 

when underneath the pole seems to cover a much larger area than 
when above it. 

12. Relation between the Distance and Apparent Size of an 
Object. — Suppose a globe of the radius BC, Fig. 2, equal to 
r. As seen from the point A its " apparent " (that is, angular) 
semi-diameter will be the angle BAG, or s, its distance being 



A 



-R- 




Fig. 2. 



AC, or R. Evidently the nearer A is to C, i.e., the smaller R 
may be, the greater will be the angle s. If the angle s is 1°, 
R will be 57.3+ times as great as r\ and if it were only 1", R 
would then be 206,265 times r. As long as the angle s does 
not exceed 1° or 2°, we may without sensible error take 

r = R x —, or U ( 



57.3 7 V206265 



The distances R and r are of course measured in units of 
length, or "linear" units, such as miles, kilometers, or feet. In 



makes it seem remoter when low down, and as the angular diameter is 
unchanged, it makes it seem to us larger (Art. 12). It may be mentioned 
as a rather curious fact that people unaccustomed to angular measure- 
ments say, on the average, that the moon (when high in the sky) appears 
about a foot in diameter. This implies that the surface of the sky appears 
to them only about 110 fret away. Probably this is connected with the 
physiological fact that by the muscular sense, by means of the convergence 
of the eyes, we can directly estimate distances up to about 100 feet with 
more or less accuracy. Beyond that wo depend for our estimate mainly 
on intervening objects. 



§ 12] CIRCLES OF THE SPHERE. 9 

general, therefore, for r, the radius 1 (in linear units) of a 
globe whose angular semi-diameter is s", we have 

r = R s " • Also s" = 206265 -• 
206265 R 

We see therefore that the apparent diameter of the object 
varies directly as the linear diameter, and inversely as the dis- 
tance. In the case of the moon, R equals about 239,000 miles, 
and r, 1081 miles ; whence, from the formula just given, her 
semi-diameter, 

•" = 206265 x J^-L 
239000 

which equals 933" — a little more than 1°. 



CIE0LES OF THE SPHEEE. 

13. In order to be able to describe intelligibly the position 
of a heavenly body in the sky, it is convenient to suppose the 
inner surface of the celestial sphere to be marked off by circles 
traced upon it, — imaginary circles, of course, like the merid- 
ians and parallels of latitude upon the surface of the earth. 
Three distinct systems of such circles are made use of, each of 
which has its own special adaptation for its special purposes. 

SYSTEM WHICH DEPENDS UPON THE DIRECTION OF THE 
FORCE OF GRAVITY AT THE POINT WHERE THE OB- 
SERVER STANDS. 

14. The Zenith and Nadir. — If we suspend a plumb-line 
(consisting simply of a slender thread with a heavy ball at- 
tached to it) , the thread will take a position depending upon 

1 The exact trigonometric equation is sins=— , whence r = H sins. 

R 
This equation is exact, even if s is a large angle. 



10 THE HORIZON. [§ 1* 

tlie direction of the force of gravit}^ If we imagine the line 
of this thread to be extended upward to the sky, it will pierce 
the celestial sphere at a point directly overhead, known as the 
astronomical zenith, 1 0T"the zenith" simply, unless some other 
qualifier is annexed. 

As will be seen later (Art. 82), the plumb-line does not point exactly 
to the centre of the earth, because the earth rotates on its axis and is 
not strictly spherical. If an imaginary line be drawn /rora the cenfre 
of the earth upward through the observer, and produced to the celes- 
tial sphere, it marks a point known as the " geocentric zenith" which is 
never very far from the astronomical zenith, but is not identical, and 
must not be confounded, with it. For most purposes the astronomi- 
cal zenith is the better practical point of reference, because its posi- 
tion can be determined directly by observation, which is not the case 
with the geocentric zenith. 

The nadir (also an Arabic term) is the point opposite to 
the zenith in the invisible part of the celestial sphere directly 
underneath. 

15. The Horizon. — If now we imagine a great circle drawn 
completely around the celestial sphere half way between the 
zenith and nadir (and therefore 90° from each of them), it 
will be the horizon. 2 Since the surface of still water, accord- 
ing to hydrostatic principles, is always perpendicular to the 
direction of gravity, we may also define the horizon as the 
great circle in which a plane, tangent to a surface of still ivater at 
the place of observation, cuts the celestial sphere; or, in slightly 
different words, the great circle where a plane passing through 
the observer's eye, and perpendicular^ to the plumb line, cuts the 
sphere. 

1 The word "zenith" is derived from the Arabic, as are many other 
astronomical terms. It is a reminiscence of the centuries when the Arabs 
were the chief cultivators of science. 

2 Pronounced ho-ri'-zon ; beware of the vulgar pronunciation hor f -f-zon. 



§15] 



VISIBLE HORIZON. 



11 



Sensible and Rational Horizon. — Many writers distinguish 
between the "sensible" and " rational " horizons, the former being de- 
fined by a horizontal plane drawn through the observer's eye, while the 
latter is defined by a plane, parallel to this, but drawn through the 
centre of the earth. Since, however, the celestial sphere is infinite in 
diameter, the two lines traced upon it by these planes, though 4000 
miles apart, confound themselves to the observer's eye into a single 
great circle, 90° from both zenith and nadir, agreeing with the first 
definition given above. The distinction is not necessary. 



16. Visible Horizon. — The word "horizon" means literally 
" the boundary" that is, the limit of landscape, where sky meets 
earth or sea ; and this boundary line is known as the Visible 
Horizon. On land it is of no astronomical importance, being 
usually an irregular line broken by hills and trees and other 
objects; but at sea it is practically a 
true circle, nearly, though not quite, 
coinciding with the horizon as above 
defined. If the observer's eye were at 
the water-level, the coincidence would 
be exact ; but if he is at an elevation 
above the surface, the line of sight 
drawn from his eye tangent to the 
water inclines or " dips " downward by 
a small angle, on account of the curva- 
ture of the earth. This is illustrated 
by Fig. 3, where OH is the line of the 
true level from the observer's eye at 0, situated at an eleva- 
tion, h, while OB is the line drawn to the visible horizon. 

The visible horizon, therefore, is not a great circle of the 
celestial sphere, but technically a small circle, parallel to the true 
horizon and depressed below it by an amount measured by the 
angle HOB, which is called the Dip of the Horizon. 1 In marine 
astronomy this visible horizon is of great importance, because 
it is the circle from which the observer measures with his 




Fig. 3. — Dip of the Horizon. 



1 The Dip (in minutes) = y/H (in feet) nearly. 



12 



VERTICAL CIRCLES, 



[§16 



sextant the height of the sun or other heavenly body, in the 
operations by which he determines the place of his ship. 

17. Vertical Circles ; the Meridian and the Prime Vertical. — 

Vertical Circles are great circles drawn from the zenith at right 
angles to the horizon. Their number is indefinite : each star 
has at any moment its own vertical circle. That particular 
vertical circle which passes north and south is known as the 
Celestial Meridian, and is evidently the circle which would be 
obtained by continuing to the sky the plane of the terrestrial 
meridian upon which the observer is located. The vertical 
circle at right angles to the meridian is the Prime Vertical. 




Fkj. 4. — The Horizon and Vertical Circles. 



0, the place of the Observer. 
OZ, the Observer's Vertical. 
Z, the Zenith; P, the Pole, 
SENW, the Horizon. 
SZPN, the Meridian. 
EZW y the Prime Vertical. 



J/, some Star. 

ZMff, arc of the Star's Vertical Circle. 

TMR, the Star's Almucantar. 

Angle TZM, or arc SH, Star's Azimuth. 

Arc HM, Star's Altitude. 

Arc ZM, Star's Zenith Distance. 



18. Parallels of Altitude, or Almucantars. — These are small 
circles of the celestial sphere drawn parallel to the horizon just 
as the parallels of latitude on the earth's surface are drawn 
parallel to the equator. The term Almueantar (Arabic) is 
seldom used. 






§ 19] ALTITUDE AND ZENITH DISTANCE. 13 

19. We care now prepared to designate the place of a body 
m the sky by telling how many degrees it is above the horizon, 
and how it " bears " from the observer. 

Altitude and Zenith Distance. — The Altitude of a celestial 
body is its angular elevation above the horizon ; i.e., the nnmber 
of degrees between it and the horizon, measured on a vertical 
circle passing through the object. In Fig. 4 the vertical circle 
ZMH passes through the body M. The arc MH measured in 
degrees is the Altitude of M, and the arc ZM (the " comple- 
ment" of MH) is called its Zenith Distance. 

20. Azimuth and Amplitude. — The Azimuth (an Arabic 
word) of a heavenly body is the same as its " bearing " in sur- 
veying ; measured, however, from the true meridian and not 
from the magnetic. 1 

It may be defined as the angle formed at the zenith between 
the meridian and the vertical circle which passes through the 
object; or, what comes to the same thing, it is the arc of the 
horizon intersected between the south point and the foot of 
this circle. In Fig. 4 SZlSTis the meridian, and the angle SZM 
is the azimuth of M, as also is the arc SH, which measures 
the angle at Z. The distance of H from the east or west point 
of the horizon is called the Amplitude of the body; HE in the 
figure is the amplitude of M. 

21. There are various ways of reckoning azimuth. Many writers 
express it in the same way as the bearing is expressed in Surveying ; 
i.e., so many degrees east or west of north or south. In the figure, the 
azimuth of M thus expressed is about S. 50° E. The more usual way 
at present, however, is to reckon it from the south point clear around 
through the west to the point of beginning. Thus an object exactly 
in the southwest would have an azimuth of 45°, while in the south- 
east it would be 315°. 

1 The reader will remember, of course, that the magnetic needle does 
not point exactly north. Its direction varies widely in different parts 
of the earth, and not only so, but it changes slightly from hour to hour 
during the day, as well as from year to year. 



14 THE POLAR SYSTEM OF CIRCLES. [§ 21 

i or example, to rind a star whose azimuth is 260° and altitude 
60°, we must face N. 80° E., and then look up two-thirds of 
the way to the zenith, the zenith distance being 30°. 

22. Altitude and azimuth, however, are for many purposes 
inconvenient, because for a celestial object they continually 
change. 

When the sun is rising, for instance, its altitude is zero. Half an 
hour later it is increased by several degrees, and the azimuth also is 
altered; for the sun does not (except to an observer at the earth's 
equator) rise vertically in the sky, but slopes upward, moving from the 
left towards the right; so also when it is setting: and the same is 
true, in a general way, of every heavenly body. 

It is desirable, therefore, to use a different way of defin- 
ing the place of a body in the heavens which shall be free 
from this objection, and this we can do by taking as the 
"fundamental line" of our system, not the direction of gravity 
as shown by the plumb-line (which is not the same at any 
two different points on the earth's surface, and is continually 
changing as tha earth turns around), but the direction of the 
earth's axis. 

SYSTEM OF CIRCLES DEPENDING ON THE DIRECTION OF 
THE EARTH'S AXIS OF ROTATION. 

23. The Apparent Diurnal Rotation of the Heavens. — If we 

go 1 out on some clear evening in early autumn and face the 
north, we shall find the aspect of that part of the heavens 
directly before us substantially as shown in Fig. 5. In the 

1 The teacher is earnestly recommended to arrange to give the class, as 
early in the course as possihle, an evening or two in the open air. It is 
the best and quickest way to secure an intelligent comprehension of the 
fundamental points and circles of the celestial sphere ; and the study of 
the constellations, though not of much account considered as astronomy, 
is always interesting to young people and awakens interest in the science. 
If the class can have access to a good celestial globe at the same time, 
it will make the exercise easier and more profitable. 



§23] 



THE CIKCUMPOLAK STARS. 



15 



northwest is the constellation of the Great Bear (Ursa Major), 
characterized by the conspicuous group of seven bright stars, 
familiar to all our readers as the " Great Dipper." It now 
lies with its handle sloping upward toward the west. The 




Fig. 5. — The Northern Circumpolar Constellations. 

two easternmost stars of the four which form its bowl are 
called the "Pointers," because they point 1 to the Pole-star, 
which is a solitary star not quite half-way from the horizon 



1 The figure is slightly wrong. They really point much more nearly 
to the Pole-star than it shows. 



1(3 THE CIKCUMPOLAR STARS. [§ 23 

to the zenith (in the latitude of New York). It is about 
as bright as the brighter of the two Pointers, and a curved 
line of small stars extending upward and westward joins 
it to the boAvl of the "Little Dipper," the Pole-star being 
at the extremity of the handle. The two brightish stars, 
which correspond in position to the Pointers in the Great 
Dipper, are known as the " Guards" (of the pole). 

High up on the opposite side of the Pole-star from the 
Great Dipper, and at nearly the same distance, is an irregular 
zigzag of five stars, about as bright as the Pole-star itself. 
This is the constellation of Cassiopeia. 

Below Cassiopeia lies Perseus ; and still lower, near the northeast- 
ern horizon, is Auriga (the Charioteer), with the bright star Capella, 
the only really first-magnitude star in all the region of the sky with 
which we are now dealing. Directly below the Pole-star the vacant 
space is occupied by the large but insignificant constellation of the 
Camelopard. Cepheus, also containing but few bright stars, is 
directly above Cassiopeia. Above the Pole-star, between it and the 
zenith, lies the head and neck of the Dragon (Draco), but its tail 
extends westward nearly half-way around the pole, and is marked by 
an irregular line of stars lying between the Great and Little Dippers. 

(The above description, and the figure given, apply strictly to the 
appearance of the heavens on Sept. 22, at 8 p.m., as seen by an 
observer in latitude 40°.) 

24. If now we watch these stars for only a few hours, we 
shall find that while all their configurations remain unaltered, 
their places in the sky are slowly changing. The Great Dip- 
per slides downward towards the north, so that by eleven 
o'clock (on Sept. 22) the Pointers are directly under the Pole- 
star. Cassiopeia still keeps opposite however, rising towards 
the zenith ; and if we continue the watch long enough, we shall 
find that all the stars appear to be moving in concentric circles 
around a point near the Pole-star, revolving counter-clockwise 
(as we look towards the north) with a steady uniform motion, 
which takes them completely around once a day, or, to be more 



§ 24] DEFINITION OF THE POLES. 17 

exact, once in 23 h 56 m 4.1 s of ordinary time. They behave just 
as if they were attached to the inner surface of a huge re- 
volving dome. 

At midnight (of Sept. 22) the position of the stars will be as indi- 
cated by the figure, if we hold it so that the XII in the margin is at 
the bottom ; at 4 a.m. they will have come to the position indicated 
by bringing XVI to the bottom ; and so on. On the next night at 8 
o'clock we shall find things (very nearly) in their original position. 

If instead of looking towards the north we now look south- 
ward, we shall find that there also the stars appear to move in 
the same kind of way. The stars which are not too near the 
Pole-star all rise somewhere in the eastern horizon, ascend 
obliquely to the meridian, and descend to set at points on the 
western horizon. The next day they rise and set again at 
precisely the same points, and the motion is always in an arc 
of a circle, called the star's diurnal circle, the size of which 
depends upon its distance from the pole. Moreover, all these 
arcs are strictly parallel to each other. 

25. The ancients accounted for these fundamental and ob- 
vious facts by supposing that the stars are really attached to 
the celestial sphere, and that this sphere really turns daily in 
the manner indicated. According to this view there must 
evidently be upon the sphere two opposite points which remain 
at rest, and these are the Poles. 

26. Definition of the Poles. — The Poles, therefore, may be 
defined as those tivo points in the sky where a star ivould have no 
diurnal motion. Its exact position may be determined with 
proper instruments by finding the centre of the small diurnal 
circle described by some star near the pole, as for instance 
the Pole-star. 1 

1 The student must be careful not to confound the pole with the Pole- 
star. The pole is an imaginary noint ; the Pole-star is only that one of the 
conspicuous stars which happens now to be nearest to that point. The 



18 



THE CELESTIAL EQUATOR. 



[§26 



This definition of the pole is that which would have been 
given by any ancient astronomer ignorant of the earth's rota- 
tion, and it is still perfectly correct. But knowing, as we now 
do, that this apparent revolution of the celestial sphere is due 
to the real rotation of the earth on its axis, we may also define 
the poles as the points where the earth's axis of rotation, pro- 
duced indefinitely, would pierce the celestial sphere. 

Since the two poles are dia- 
metrically opposite in the sky, 
only one of them is usually vis- 
ible from any given place. Ob- 
servers north of the earth's 
equator see only the north pole, 
and vice versa for observers in 
the southern hemisphere. 

27. The Celestial Equator, or 
Equinoctial. — This is a great 
circle of the celestial sphere, 
drawn half-way between the poles 
(therefore everywhere 90° from 
each of them), and is the great circle in which the plane of the 
earth's equator cuts the celestial sphere. It is often called the 
"Equinoctial." Fig. 6 shows how the plane of the equator 
produced far enough would mark out such a circle in the 
heavens. 




Fig. 6. — The Plane of the Earth's Equa 
tor produced to cut the Celestial Sphere. 



The equator cuts the horizon at the east and west points, but it 
does not cut it perpendicularly nor pass through the zenith unless the 



Pole-star (at present) is about 1J° distant from the pole. If we draw an 
imaginary line from the Pole-star to the star Mizar (Zeta Ursa? Majoris, 
the one at the bend of the Dipper handle), it will pass almost exactly 
through the pole itself; the distance of the pole from the Pole-star being 
very nearly one-quarter of the distance between the two "Pointers." 



§ 281 HOUR-CIRCLES. 19 

observer is at the earth's equator ; at its highest point it is just as 
far below the zenith as the pole is above the horizon. 

28. Parallels of Declination. — Small circles drawn parallel 
to the equinoctial, like the parallels of latitude on the earth, 
are known as Parallels of Declination. For any star situated 
on one of these parallels, the parallel is obviously identical 
w r ith the star's diurnal circle. (The reason why these circles 
in the heavens are not called parallels of latitude will appear 
later.) 

29. Hour-Circles. — The great circles of the celestial sphere 
which pass through the poles, like the meridians on the earth, 
and are therefore perpendicular to the celestial equator (" sec- 
ondaries " to it), are called Hour-Circles. Some writers call 
them celestial "meridians " but the term is objectionable, since 
it is sometimes used to designate an entirely different set of 
circles (the secondaries to the ecliptic — Art. 38). That par- 
ticular hour-circle which passes through the zenith at any 
moment is of course coincident with the Celestial Meridian, 
defined in Art. 17. 

30. The Celestial Meridian and the Cardinal Points. — The 

best form for the definition of the Celestial Meridian is, the 
great circle ivhich passes through the zenith and the poles. The 
points where this meridian cuts the horizon are the north and 
south points, and the east and west points of the horizon lie 
half-way between them ; the four being known as the Cardinal 
Points. The student is especially cautioned against confound- 
ing the North Point with the North Pole; the former being on 
the horizon, the latter high up in the sky. 

In Fig. 7 P is the north celestial pole, Z is the zenith, and SQZPN 
is the celestial meridian. PmP' is the hour-circle of the object m, 
and am lib V is its parallel of declination or diurnal circle. NESW is 
the horizon, and the points indicated by these letters are the four 
Cardinal Points. 



20 



DBCUNATION AND POIiAB DISTANCE. 



[| 30 



By means of the hour-circles and the celestial equator we 
now have a second method of designating the position of an 
object in the heavens : for Altitude and Azimuth we can sub- 
stitute Declination and Hour-Angle. 



31. Declination and Polar Distance. — The Declination of a 
star is its angular distance north or south ofthecelesti 

+ if north. — if south. It corresponds precisely with the 
L ' f a place on the earth's surface ; it cannot, however, 



R? 




p 



*\ 




\ \ 
\ v. 


V 


\ 


\ 
\ 


\ 

V 


\ 

\ 




\ / 




\ 


\ 













Fi'T. 7. — Hour-CireU- 



e of the Observe r : Z. his Zenith. 
SBNW, the Hoi:. 
POP', line parallel to the Axis of tV 
P and P\ i. 

r, the Celestial Equator, or Equinoc- 

X, the Vernal Equii 



- ime Star. 
Star's 

I - 
Angle m PP = arc QY. the St.-.. a 

Hour-Anoh'; =24* minus Star's 
^western^ Ho 
Angle XP i=arcXJ r t 8Ur , a Right 

sion. Sidereal lime at the moment 



PXP', the Equinoctial Colore, or .". 
Hour-Circle. 



Mm XPQ. 



be call. I stdal "Latitude," because that term has been pre- 
occupied by an entirely different quantity (Art. 38 

[nFig. 7,m7 is the declination P : - its North 



§ S2J THE VERNAL EQUINOX. 21 

32. Hour-Angle. — The Hoar-Angle of a star at any moment 
is the angle at the pole between the celestial meridian and the 
hoar-circle of the star, which angle is measured by the arc 
of the celestial equator intercepted between the hour-circle of the 
star and the meridian. In Fig. 7, for the body m, it is the 
angle mPZ, or the arc Q Y. This angle (or arc) may of course 
be measured like any other, in degrees; but since it depends 
upon the time which has elapsed since the body was last on 
the meridian, it is more usual to measure it in hours, minutes, 
and seconds of time. The " hour " is then equivalent to -^ of 
a circumference, or 15°, and the minute and second of time to 
15 minutes and 15 seconds of arc respectively. Thus an hour- 
angle of 4 h 2 m 3 s equals 60° 30' 45". 

33. The position of the body m (Fig. 7) is, then, perfectly denned 
by saying that its declination is + 25°, and its hour-angle 40° east (or 
simply 320° if we choose to reckon completely around in the direction 
of the diurnal motion). Instead of 40 degrees, we might say 2 h 40 m 
east, or 21 h 20 m to correspond to the 320°. 

The declination of a star (omitting certain minutiae for the 
present) remains practically unaltered even for years, but 
the hour-angle changes continually and uniformly at the rate 
of 15° for every (sidereal) hour. 

34. The Vernal Equinox, or First of Aries. — The sun and 

the planets do not behave as if they were firmly fixed upon 
the celestial sphere like the stars ; but rather as if they were 
glow worms crawling slowly about upon its surface while it 
carries them in its diurnal rotation. As every one knows, the 
sun in the winter is far to the south of the equator, and in 
the summer far to the north ; it crosses the equator, therefore, 
twice a year, passing from the south to the north about March 
20th, and always at the same point (neglecting for the present 
the effect of what is known as precession, Art. 122). This 
point is known as the Vernal Equinox, or the First of 



22 EIGHT ASCENSION. f§ 34 

Aries, and is made the starting-point for certain important 
systems of celestial measurement. It is the "Greenwich" of 
the celestial sphere. 

Unfortunately it is not marked by any conspicuous star ; but a line 
drawn from the Pole-star through Beta Cassiopeia? (the westernmost 
or "preceding" star in the zigzag) (see Fig. 5, Art. 23) and continued 
90° from the pole, strikes very near it. 

35. Sidereal Time. — A sidereal clock is one that is set and 
rated so that it marks noon every day, not at the moment 
when the sun is crossing the meridian, bnt when the vernal 
equinox does so. When the clock is correct {i.e., neither too 
fast or slow), its face indicates the hour-angle of the vernal 
equinox; and we may therefore define the sidereal time at 
any moment as the hour-angle of the vernal equinox at 
that moment. 

It is called u sidereal " time because the length of its dav is the time 
that elapses between two successive passages of the same star across 
the meridian. It is not convenient for the purposes of ordinary life ; 
but for many astronomical purposes it is not only convenient, but 
practically indispensable. It is usual to divide the face of the sidereal 
clock into 24 hours, and to reckon the time completely around, instead 
of counting it in two half-days of 12 hours each; moreover, its day, 
for reasons which will be explained later (Art. 128), is about four min- 
utes shorter than the ordinary solar day. 

36. Right Ascension. — The "Right Ascension" of a star may 
now be defined as the angle made at the celestial pole between the 
hour-circle of the star and the hour-circle which passes through the 
vernal equinox, and is known as the Equinoctial Colure. This 
angle is measured by the arc of the celestial equator intercepted be- 
tween the vernal equinox and the point where the star's hour-circle 
cuts the equator, and is reckoned always eastward from the 
equinox completely around the circle, and may be expressed 
either in degrees or in hours. A star one degree ivest of the 



§ 36] CELESTIAL LATITUDE AND LONGITUDE. 23 

equinox has a right ascension of 359°, or 23 hours and 56 
minutes. 

Evidently the diurnal motion does not affect the right ascension of 
a star, but, like the declination, it remains practically unchanged for 
years. In Fig. 7, if X be the vernal equinox, the right ascension of 
m is the angle XPm, or the arc XY measured from X eastward. 

37. Observatory Definition of Right Ascension. — The right 
ascension of a star may also be correctly, and for many pur- 
poses most conveniently, defined, as the sidereal time at the 
moment when the star is crossing the meridian. 

Since the sidereal clock is made to show zero hours, minutes, and 
seconds at the moment when the vernal equinox is on the observer's 
meridian, its face at any other time shows the hour-angle of the 
equinox ; and this is just what was denned in the preceding section 
as the right ascension of any star which may then happen to be on 
the meridian. 

Obviously the positions of the heavenly bodies with refer- 
ence to each other may be indicated by their declinations and 
right ascensions, just as the positions of places on the earth's 
surface are indicated by their latitudes and longitudes. The 
declination of a star corresponds exactly to the latitude of a 
city, and the star's right ascension to the city's longitude; the 
vernal equinox taking, in the sky, the place of Greenwich on 
the earth. 

38. Celestial Latitude and Longitude. — A different way of 
designating the positions of heavenly bodies in the sky has 
come down to us from very ancient times. Instead of the 
equator, it makes use of another circle of reference in the sky 
known as the Ecliptic. This is simply the apparent path de- 
scribed by the sun in its annual motion among the stars, and 
may be defined as the intersection of the plane of the earth's orbit 
with the celestial sphere, the " vernal equinox " being the place 



24 RECAPITULATION. [§ 38 

in the sky where the celestial equator crosses this ecliptic. 
Before the days of clocks, the ecliptic was in many respects 
a more convenient circle of reference than the equator, and 
was almost universally used as such by the old astronomers. 
Celestial latitude and longitude are measured with reference to 
the ecliptic in the same way that right ascension and declina- 
tion are measured with respect to the equator. Too much 
care cannot be taken to avoid confusion between terrestrial 
latitude and longitude and the celestial quantities that bear 
the same name (Appendix, Art. 491). 

39. Recapitulation. — The direction of gravity at the point 
where the observer happens to stand determines the zenith and 
nadir, the horizon and the almucantars (parallel to the hori- 
zon), and all the vertical circles. One of the verticals, the me- 
ridian, is singled out from the rest by the circumstance that it 
jxisses through the pole, thus marking the north and south 
points where it cuts the horizon. Altitude and azimuth (or 
their complements, zenith distance and amplitude) are the " co- 
ordinates " which designate the position of a body by reference 
to the zenith and meridian. 

Evidently this set of points and circles shifts its position 
with every change in the place of the observer. Each place 
has its own zenith, its own horizon, and its own meridian. 

In a similar way. the direction of the earth's axis (which is 
independent of the observer's place on the earth) determines 
the poles (Art. 26), the equator, the parallels of declination, and 
the hour-circles. Two of these hour-circles are singled out as 
reference lines: one of them is the meridian which passes 
through the zenith, and is a purely local reference line ; the 
other, the equinoctial colure, which passes through the vernal 
equinox, a point chosen from its relation to the sun's annual 
motion. 

Declination and hour-angle define the place of a star with 
reference to the pole and the meridian, while declination and 



§39] 



THE POLE AND LATITUDE. 



25 



right ascension refer it to the pole and vernal equinox. The 
latter are the co-ordinates ordinarily given in star-catalogues 
and almanacs for the. purpose of defining the position of stars 
and planets, and they correspond exactly to latitude and lon- 
gitude on the earth, by means of which geographical positions 
are designated. 



Finally, the earth's orbital motion gives us the great circle of the sky 
known as the ecliptic, and celestial latitude and longitude ave quantities 
which define the position of a star with reference to the ecliptic and 
the vernal equinox. For most purposes this pair of co-ordinates is 
practically less convenient than right ascension and declination ; but, 
as has been said, it came into use much earlier, and is not without its 
advantages in dealing with the planets and the moon. 

40. Relation of the Place of the Celestial Pole to the Ob- 
server's Latitude. — If an observer were at the north pole of 
the earth, it is clear that the Pole-star would be very near his 
zenith, while it would be at the horizon if he were at the 
equator. The place of the pole in the sky, therefore, depends 
evidently on the observer's latitude, and in this very simple 
way — The Altitude of the Pole (its height in degrees 
above the horizon) is 
always equal to the 
Latitude of the Ob- 
server. This relation 
will be clear from Fig. 8. 
The latitude (astronomi- 
cal) of a place may be 
defined as the angle be- 
tween the direction of 
gravity at that place and 
the plane of the earth's 

equator, — the angle ONQ FlG - 8. -Relation of Latitude to the Elevation 
., n T p of the Pole. 

in the figure. It, now, 

at we draw HIT perpendicular to ON, it will be a " level " 




26 THE RIGHT SPHERE. [§ ^ 

line, and will lie in the plane of the horizon. From also 
draw OP" parallel to CP', the earth's axis. Both OP" and CP ] 
being parallel, will be directed to the same " vanishing-point " 
in the celestial sphere, (Art. 8), and this point is the celestial 
pole (Art. 26). 

The angle H'OP" is therefore the altitude of the pole 
as seen at 0; and it obviously equals ONQ, since OH' is per- 
pendicular to ON, and both OP 1 and OP" are perpendicular 
to QQ'. 

This fundamental relation, that the altitude of the pole is iden- 
tical with the observer's latitude, cannot be too strongly impressed 
on the mind. 

41. The Right Sphere. — If the observer is situated at the 
earth's equator (that is, in latitude zero), the pole will be in his hori- 
zon, and the celestial equator will be a vertical circle, coinciding with 
the "prime vertical" (Art. 17). All heavenly bodies will rise and set 
vertically instead of obliquely, as in our own latitudes; and their 
diurnal circles will all be bisected by the horizon, so that they will be 
12 hours above and 12 hours below it, and the length of the night will 
always equal that of the day. This aspect of the heavens is called 
the Right Sphere. 

42. The Parallel Sphere. — If the observer is at the pole of the 
earth, where his latitude equals 90°, then the celestial pole will be at 
the zenith, and the equator will coincide with the horizon. If he is at 
the north pole, all the stars north of the celestial equator will remain 
permanently above the horizon, never rising nor setting, but sailing 
around the sky on parallels of altitude. The stars in the southern 
hemisphere, on the other hand, will never rise to view. 

Since the sun and moon move among the stars in such a way that 
during half the time they are north of the equator and half the time 
south of it, they will be half the time above the horizon and half 
the time below it (at least approximately, since this statement needs to 
be somewhat modified to allow for the effect of "refraction" — Art. 
50). The moon will be visible for about a fortnight at a time, and 
the sun for about six months. 



§42] 



THE OBLIQUE SPHERE. 



27 




Fig. 9. — The Oblique Sphere. 



It is worth noting that for an observer exactly at the north pole 
the definitions of meridian and azimuth break down, since there the 
zenith coincides with the pole. Face in what direction he will, he is 
looking due south. If he 
changes his place a few steps, 
however, everything will come 
right. 

43. The Oblique Sphere. 

— At any station between 
the pole and the equator 
the pole will be at an eleva- 
tion above the horizon, and 
the stars will rise and set 
in oblique circles, as shown 
in Fig. 9. Those whose 
distance from the elevated 
pole is less than FN, the 
latitude of the observer, 
will of course never set, remaining perpetually visible. The 
radius of this " circle of perpetual apparition," as it is called 
(the shaded cap around P in the figure), is obviously just 
equal to the height of the pole, becoming larger as the latitude 
increases. On the other hand, stars within the same distance 
of the depressed pole will lie within the " circle of perpetual 
occultation," and will never rise above the horizon. 

A star exactly on the celestial equator will have its diurnal 
circle, EQ WQ 1 , bisected by the horizon, and will be above the 
horizon just as long as below it. A star north of the equator 
(if the north pole be the elevated one) will have more than 
half of its diurnal circle above the horizon, and will be visible 
for more than twelve hours of each day; as, for instance, a 
star at A, — and of course the reverse will be true of the stars 
on the other side of the equator. Whenever the sun is north 
of the celestial equator, the day will therefore be longer than 
the night for all stations in northern latitude ; how much 



28 THE OBLIQUE SPHERE. [§ 43 

longer will depend both on the latitude of the place and the 
sun's distance from the equator (its declination). 

44. Whenever the sun is north of the equator, it will, in northern 
latitudes, rise at a point north of east, as B in the figure, and will 
continue to shine upon every vertical surface that faces the north, 
until, as it ascends, it crosses the prime-vertical EZ W at some point 
V. In the latitude of New York the sun on the longest days of sum- 
mer is south of the prime-vertical only about eight hours of the whole 
fifteen during which it is above the horizon. During seven hours of 
the day it shines into north windows. 

If the latitude of the observer is such that PN in the figure is 
greater than the sun's polar distance at the time when it is farthest 
north, the sun will make a complete circuit of the heavens without 
setting, as is the case at the North Cape and at all stations within the 
Arctic Circle. (See Art. 130.) 

45. A celestial globe will be of great assistance in studying 
these diurnal phenomena. The north pole of the globe must 
be elevated to an angle equal to the latitude of the observer, 
which can be done by means of the degrees marked on the 
metal meridian ring. It will then be seen at once what stars 
never set, which ones never rise, and during what part of the 
24 hours any heavenly body at a known distance from the 
equator is above or below the horizon. 

(For a description of the Celestial Globe, see Appendix, Art. 521.) 



§ 46] PRACTICAL PROBLEMS. 29 



t 



CHAPTER II. 






FUNDAMENTAL PROBLEMS OF PRACTICAL ASTRONOMY. — 
THE DETERMINATION OF LATITUDE; OF TIME; OF 
LONGITUDE; OF THE PLACE OF A SHIP; OF THE POSI- 
TION OF A HEAVENLY BODY. 

46. There are certain problems of Practical Astronomy 1 
which are encountered at the very threshold of all investiga- 
tions respecting the dimensions and motions of the heavenly 
bodies, the earth included. An observer must know how to 
determine his 'position on the surface of the earth, how to ascer- 
tain the exact time at which an observation is made, and how to 
observe the precise position of a heavenly body, and fix its right 
ascension and declination. 

The first of these practical problems which we are to con- 
sider is 

47. The Determination of the Observer's Latitude. — In Geog- 
raphy the latitude of a place is usually defined simply as its 
distance north or south of the earth's equator, measured in 
degrees. This is not explicit enough, unless it is stated how 
the degrees themselves are to be measured. If the earth were 
a perfect sphere, there would be no difficulty. But since the 
earth is quite sensibly flattened at its poles, the degrees (geo- 
graphical) have somewhat different lengths in different parts 
of the earth. 



1 Practical Astronomy is that branch of Astronomy which treats of the 
methods of making astronomical observations, the instruments used, and 
the calculations by which the results are deduced. 




30 PRACTICAL ASTRONOMY. [§ 47 

Aii exact definition of the astronomical latitude of a place 
has already been given (Art. 40). It is (1) the angle betv>: 
the direction of gravity and the plane of the equator, which is 
the same as the altitude of the pole. (2) It may also be defined 

as the declination of the zenith, as 
is clear from Fig. 10. where PB. 
the altitude of the pole, equals 
QZ (since PQ and ZB are each 
90°), and QZ by the very defini- 
_ B tion of declination (Art. 31) is 
. , T , the declination of the zenith. The 

Fig. 10. — Determination of Latitude. 

problem, then, is to det ermine, 
by observing some of the heavenly bodies, either the angle 
of elevation of the celestial pole, or the distance in degr-— 
between the zenith and the celestial equator. 

48. First Method. — By circumpolars. The most obvious 
method is by observing with a suitable instrument the altitude 
of some star near the pole (a •• circumpolar '* at the 
moment when it is crossing the meridian above the pole, and 
again 12 (sidereal) hours later when it is once more on the 
meridian below the pole. In the first case its elevation is the 
greatest possible; in the second, the least possible. The mean 
of the two altitudes (each corrected for atmospheric refraction, 
which will shortly be considered) is the latitude of the o\ 

The method has the great advantage that it is an •• iudependei* 
one : i.e.. the observer is not obliged to make use of any data that 
have been determined by his predecessors. But the method fails for 
stations very near the equator of the earth. 

49. The Meridian Circle. — The instrument with which such 
observations are usually made in a fixed observatory is called the 
meridian circle. The principle of it is exhibited in Fig. 11. It con- 

- of a telescope firmly i to a stiff axis, which turns in bear- 

ings attached to two -..lid piers. These bearings are so adjusted that 



»] 



DETERMINATION OF LATITUDE. 



31 



the axis is exactly level and exactly east and west. Xear E, at the 
eye end of the instrument, a " reticle " of spider-lines (see Appendix, 
Art. 544) is so placed in the tube that on looking into the eye-piece it 
can be distinctly seen at the same time with the star which is to be 
observed — the field of view 
being slightly illuminated so 
that the spider-threads ap- 
pear like dark lines drawn in 
the sky. 

The telescope as it is ro- 
tated up or down upon the 
pivots is obviously always di- 
rected to the meridian ; and 
by elevating or depressing 
it, it can be so set that any 
given star will be " bisected " 
by the horizontal spider-line 
of the reticle at the moment 
when it crosses the meridian. 
The instrument carries a 
large and carefully graduated ' 
circle so attached to the axis 
as to turn with the telescope, 
scopes 




Fig. 11. 



•The Meridian Circle (Schematic). 

Two or more so-called "reading micro- 
fixed to the pier "read off" the graduation of this circle, and 
so determine the altitude of the object at which the telescope is pointed. 
(A fuller account of the instrument and its appendages is given in the 
Appendix, Art. 548.) 



50. Refraction. — It was said that the observed altitudes must be 
corrected for atmospheric refraction. As the rays of light enter the 
earth's atmosphere from a distant object they are bent downward by 
refraction (Physics, page 347), except only such as strike the surface 
of the atmosphere perpendicularly. Fig. 12 illustrates this effect. 
Since the observer sees the object in the direction in which the raijs 
enter the eye, without any reference to its real position, this bending 
down of the rays causes every object seen through the air to look 
higher up in the sky than it would if the air were absent. 

Under average conditions the refraction elevates a body at the 
horizon about 35', so that the sun and moon in rising both appear 



32 



KEFPvACTION. 



[§50 



clear of the horizon while still wholly below it. At an altitude 
of only 5° the refraction falls off: to 10' ; at 44°, it is 1'; and at 

the zenith, zero. Its amount at any 
given altitude varies quite sensibly how- 
ever, with the temperature and barometric 
pressure, increasing as the thermome- 
ter falls or as the barometer rises ; so 
that whenever great accuracy is re- 
quired in measures of altitude of a 
heavenly body, we must have observa- 
tions both of the thermometer and 
barometer to go with the readings of 
the "circle." In works on Practical 
Astronomy tables are given by which the refraction can be computed 
for an object at any altitude and in any state of the weather. 

It is hardly necessary to say that this indispensable " refraction- 
correction " of nearly all astronomical observations makes a great deal 
of trouble and involves more or less error and uncertainty. 




Fig. 12. 



51. Second Method of Determining the Latitude. — By the 

meridian altitude or zenith distance of a body ivhose declination 
is accurately known. 

In Fig. 13 the circle AQPB is the meridian, Q and P being 
respectively the equator and the 
pole, and Z the zenith. QZ is 
obviously the declination of the 
zenith, or the latitude of the ob- 
server (Art. 47). Suppose now 
that Ave observe Zs, the zenith 
distance of a star, s, south of the 
zenith as it crosses the meridian, 

and that Qs, the declination of the star, is known. Then, evi- 
dently, QZ equals Qs -\- sZ\ i.e., the latitude equals the declina- 
tion of the star plus its zenith distance. 

If a star were at s', south of the equator, the same equation would 
still hold algebraically, because the declination Qs' is a minus quantity. 




§ 51 J DIFFERENT KINDS OF TIME. 33 

If the star were at n, between the zenith and pole, we should have, lati- 
tude equals the declination minus the zenith distance. 

If we use the meridian circle in making our observations, we can 
always select stars that pass near the zenith where the refraction is 
small, which is in itself an advantage. Moreover, we can select the 
stars in such a way that some will be as much north of the zenith as 
others are south, and this will "eliminate" the refraction errors. On 
the other hand, in using this method we have to obtain our star decli- 
nations from the catalogues made by previous observers, and so the 
method is not an "independent " one. 

There are many other methods in use, some of which are 
practically more convenient and accurate than either of the 
two described, but their explanation would take us too far. 

See Art. 71* for a note upon Variation of latitude. 

DIFFERENT KINDS OF TIME. 

52. Time is usually defined as " measured duration" From 
the earliest history the apparent diurnal rotation of the 
heavens has been accepted as the standard, and to it we refer 
all artificial measures of time, such as clocks and watches. In 
practice the accurate " determination of time " therefore con- 
sists in finding the hour- angle of the object ivhich has been 
selected to mark the beginning of the day by its " transit " ac7*oss 
the meridian. 

In Astronomy, three kinds of time are now recognized, — 
Sidereal Time, Apparent Solar Time, and Mean Solar 
Time, the last being the time of civil life and ordinary busi- 
ness, while the first is most used for astronomical purposes. 
Apparent solar time has now practically fallen out of use, 
except in half-civilized countries where w^atches and clocks 
are scarce and sun-dials are still the principal time-keepers. 

53. Sidereal Time. — The celestial object which determines 
sidereal time by its position in the sky at any moment is, it 



34 SIDEREAL AND SOLAR TIME; [§ & 3 

will be remembered, the te vernal equinox" or u first of Aries"; 
i.e., tlie point where the sun crosses the celestial equator about 
March 20th every year (Art. 34). As has already been ex- 
plained (Art. 35), the sidereal time at any moment is, there- 
fore, the hour-angle of the vernal equinox at that moment; or, 
what comes to the same thing, it is the time marked by a 
clock which is so set and adjusted as to show (sidereal) noon 
(0 h , m , s ) at each transit of the " first of Aries." The sidereal 
"day" is the interval between successive transits of this 
point, and within less than y i r) of a second, is equal to the 
interval between successive transits of any given star. The 
equinoctial point is, it is true, invisible ; but its position 
among the stars is always known, so that its hour-angle can 
be determined by observing them. 

54. Apparent Solar Time. — Just as sidereal time is the 
hour-angle of the vernal equinox, so apparent solar time at any 
moment is the hour-angle of the sun. It is the time shot/on by 
the sun-dial, and its "noon" occurs at the moment when the 
sun crosses the meridian. On account of the annual eastward 
motion of the sun among the stars, due to the earth's orbital 
motion (more fully explained farther on — Art. 128), the 
day of solar time is about four minutes longer than the side- 
real day. Moreover, because the sun's motion in the sky is 
not uniform, the days of apparent solar time are not all of 
the same length. December 23d, for instance, is 51 seconds 
longer from noon to noon, reckoned by the sun, than Sept. 
16th. For this reason, apparent solar time is unsatisfactory 
tor scientific use, and it has been discarded in favor of mean 
solar time. 

55. Mean Solar Time. — X. fictitious sun is therefore imag- 
ined, which moves around the sky uniformly^ and in the celestial 
equator, completing its annual course in exactly the same time 



§ 55] CIVIL DAY — ASTKONOMICAL DAY. 35 

as that in which the actual sun makes the circuit of the eclip- 
tic, that is, in one year; and this "fictitious sun" is made the 
time-keeper for mean solar time. The mean solar days are 
therefore all exactly of the same length, and equal in length 
to the average "apparent solar" day. It is mean noon when this 
" fictitious sun " crosses the meridian, and at any moment the 
hour-angle of the ''fictitious sun" is the mean time for that 
moment. 

56. Sidereal time will not answer for business purposes, because 
its noon (the transit of the vernal equinox) occurs at all hours of the 
day in different seasons of the year. On the 22d of September, for 
instance, it comes at midnight. Apparent solar time is unsatisfactory 
from the scientific point of view, because of the variation in the 
length of its days and hours. And yet we have to live by the sun : its 
rising and setting, daylight and night, control our actions. In mean 
solar time we find a satisfactory compromise — a time-unit which is 
invariable, and still in agreement with sun-dial time nearly enough for 
convenience. It is the time now used for all purposes except in cer- 
tain astronomical work. The difference between apparent time and 
mean time, (never amounting to more than about a quarter of an hour,) 
is called the " equation of time" and will be discussed hereafter in con- 
nection with the earth's orbital motion (Art. 128). The Nautical 
Almanac also furnishes data by means of which the sidereal time 
may be accurately deduced from the corresponding solar time, or vice 
versa, by a very brief x calculation. 

57. The Civil Day and the Astronomical Day. — The astro- 
nomical day begins at "mean noon"; the civil day, 12 hours 
earlier at midnight. Astronomical mean time is reckoned 
around through the whole 24 hours instead of being counted 
in two series of 12 hours each : thus, 10 a.m. of Wednesday, 

1 The approximate relation between sidereal and mean solar time is very 
simple. On March 20th, the two times agree, and after that the sidereal 
time gains two hours a month. On April 5th, therefore, the sidereal 
clock is one hour in advance, on April 20th, two hours, and so on. 



36 



DETERMINATION OF TIME. 



[§57 



Feb. 27th, civil reckoning, is Tuesday, Feb. 26th, 22 hours, by 
astronomical reckoning. Beginners need to bear this in mind 
in referring to the almanac. 1 

DETERMINATION OF TIME. 

58. In practice the problem of determining time always 
takes the form of ascertaining the "error" or "correction" of 
a time-piece ; that is, finding the amount by which a watch or 
clock is faster or slower than the time it ought to indicate. 

The method ordinarily em- 



sCCuti 



y 



ployed by astronomers is by 
means of the Transit Instru- 
ment, which is an instrument 
precisely like the meridian 
circle (Art. 49) without the 
circle and its reading micro- 
scopes. As the instrument 
(Fig. 14) is turned upon its 
axis, the vertical wire in the 
centre of the " reticle " exact- 
ly follows the meridian, when 
the instrument is in perfect 
adjustment. If, then, we know 
the instant shown by the 
clock when a known star is crossing this wire, we have at 
once the means of determining the error of the clock, because 
the sidereal time at that moment is equal to the star's right 
ascension (Art. 37). The difference between the right ascen- 
sion of the star as given in the almanac and the time shown 
by the face of the clock at the moment of transit gives directly 
the "error" of the sidereal clock. 

The observation of only a single star would give the error of the 
clock pretty closely, but it is much better and usual to observe a nuin- 



Fig. 14. — The Transit Instrument. 



1 A movement is on foot, and not unlikely to succeed, to make the 
astronomical day begin at midnight after 1900. 



§ 58] DETERMINATION OF TIME. 37 

ber of stars (from 8 to 10), reversing the instrument upon its pivots 
once at least during the operation. With a good instrument a skilled 
observer can thus determine the clock error within about a thirtieth 
of a second of time, provided proper means are taken to allow for his 
" personal equation." 

If instead of observing a star we observe the sun with this instru- 
ment, the time shown by the (solar) clock ought to be noon plus or 
minus the equation of time for the day as given in the almanac. But 
for various reasons transit observations of the sun are less accurate 
than those of the stars, and it is better to deduce the mean solar time, 
when needed, from the sidereal by means of the almanac data. (For 
a fuller description of the transit instrument and its adjustments see 
Appendix, Art. 544.) 

59. Personal Equation. — It is found that every observer has 
his own peculiarities of time-observation, and the so-called "personal 
equation " of an observer is the amount that must be added (algebraically) 
to the time observed by him in order to get the actual moment of transit. 
This personal equation differs for different observers, but is reason- 
ably constant (though never strictly so) for one who has had sufficient 
practice. In the case of observations with the chronograph (see 
Appendix, Art. 547) it is usually less than 0.1 of a second. 

One of the most important problems of practical astronomy now 
awaiting solution is the contrivance of some convenient method of time- 
determination which shall be free from this annoying human element. 

60. Other Methods of Determining Time. — While the method 
by the transit instrument is most used, and is on the whole the most 
convenient and accurate, several other methods are available. At sea, 
and by travellers on scientific expeditions, the time is usually deter- 
mined by observing the altitude of the sun some hours before or after 
noon (see Appendix, Art. 493). It can also be done roughly by means 
oi a noon-mark, which is simply a true north and south line running 
from the bottom of some vertical line, — a line drawn on the floor 
from the edge of the door-jamb, for instance. The moment when 
the shadow falls on this line is apparent noon, and must be corrected 
for the equation of time to get mean noon. As the shadow is some- 
what indistinct, a determination made in this way is liable to an error 
of half a minute or so. 



38 LONGITUDE. [§ «1 



LONGITUDE. 

61. Having now the means of finding the true local time, 
we can approach the problem of the longitude, in many re- 
spects the most important of what may be called the' " eco- 
nomic" problems of Astronomy. The great observatories of 
Greenwich and Paris were founded expressly to furnish the 
necessary data for determining the longitude of ships at sea, 
and the English government has given large prizes for the 
construction of clocks and chronometers to be used in such 
determinations. 

The longitude of a place on the earth may be defined as 
the angle (at the pole of the earth) between the standard l merid- 
ian and the meridian passing through the place ; and this of 
course is equal to the arc of the equator intercepted between the 
two meridians. 

Since the earth turns uniformly on its axis, this angle is 
strictly proportional to, and is measured (in time-units — Art. 
32) by the time intervening between the transits of any given 
star across the two meridians. It may therefore be defined as 
the difference of local times between the standard meridian and 
the place in question, or the amount by which noon at Green- 
wich is earlier or later than noon at the station of the observer. 
Accordingly, terrestrial longitude is now usually reckoned in 
hours, minutes, and seconds rather than in degrees. 

Since an observer can easily find his own local time by the 
methods given above, the knot of the problem is simply this : 
To find Greenwich local time at any moment without going 
there. 

62. First Method. — By Telegraph. Incomparably the best 
method, whenever it is available, is to make a direct telegraphic 

1 As to the standard meridian, there is some variation of usage among 
different nations. The French reckon from Paris, but most other nations 
use the meridian of Greenwich. 



§ 62] LONGITUDE: 39 

comparison between the clock of the observer and that of some 
station the longitude of which is known. The difference 
between the two clocks will be the true difference of longitude 
of the places after the proper corrections for their errors and 
" personal equation" (Art. 59) have been applied. 

The astronomical difference of longitude between two places can 
thus be determined by four or five nights' observations within about 
sV P ar t °f a second of time ; that is, within 20 feet or so, in the lati- 
tude of the United States. 

63. Second Method. — By the Chronometer. The chronome- 
ter is merely a very accurate watch. It is set to Greenwich 
time at some place whose longitude is known, and thereafter 
keeps that time wherever carried. The observer has only to 
find the apparent " error " of such a chronometer with respect 
to his local time, and this apparent error is his longitude. 

Practically, of course, no chronometer goes absolutely without gain- 
ing or losing ; hence it is always necessary to know and allow for its 
gain or loss since the time it was set. Three or more should 
be used if possible, since any irregular going of either of them will 
then be pretty surely indicated by its disagreement with the others. 

64. Other Methods. — Before the days of telegraphs and reliable 
chronometers, astronomers were generally obliged to get their Green- 
wich time from the moon, which may be regarded as a clock-hand 
with stars for dial figures. Since the laws of the moon's motion are 
now well known, so that the place which the moon will occupy is pre- 
dicted in the Nautical Almanac for every hour of every Greenwich 
day, it is possible to deduce the Greenwich time at any moment when 
the moon is visible, by some observation w T hich will determine her 
place among the stars. The almanac place, however, is the place at 
which the moon w^ould be seen by an observer situated at the centre of 
the earth, and consequently the actual observations in most cases re- 
quire rather complicated and disagreeable reductions before they can 
be made available. 



40 LOCAL AND STANDARD TIME. [§ 64 

Various kinds of observations of the moon are made use of for the 
purpose, of which the most satisfactory are those obtained on occa- 
sions when the moon " occults " a star or eclipses the sun. For fuller 
explanations, see " G-eneral Astronomy." 

65. Local and Standard Time. — Until recently it has been 
always customary to use local time, each, station determining 
its own time by its own observations. Before the days of the 
telegraph and while travelling was comparatively slow and 
infrequent, this was best. At present, for many reasons, it is 
better to give up the old system of local times in favor of a 
system of standard time. The change facilitates all railway 
and telegraphic business in a remarkable degree, and makes it 
practically easy for. every one to keep accurate time, since it 
can be daily wired from some observatory to every telegraph 
office. According to the system now established in North 
America, there are five such standard times in use, — the 
colonial, the eastern, the central, the mountain, and the Pacific, 
— which differ from Greenwich time by exactly 4, 5, 6, 7, and 
8 hours respectively, the minutes and seconds being everywhere 
identical. 

At most places only one of these standard times is employed ; but 
in cities where different systems join each other, as for instance at 
Atlanta and Pittsburgh, there are two standard times in use, differ- 
ing from each other by exactly one hour, and from the local time by 
about half an hour. In some such places the local time also main- 
tains itself. 

Tn order to determine the standard time by observation, it is only 
necessary to determine the local time by one of the methods given, 
and correct it according to the observer's longitude from Greenwich. 

66. Where the Day begins. — It is evident that if a travel- 
ler were to start from Greenwich on Monday noon and travel 
westward as fast as the earth turns to the east beneath his 
feet, he would keep the sun exactly upon the meridian all day 
long and have continual noon. But what noon ? It was 



§ 66] PLACE OF A SHIP AT SEA. 41 

Monday when lie started, and when he gets back to London 
24 hours later it will be Tuesday noon there ; and yet he has 
had no intervening night. When did Monday noon become 
Tuesday ? 

It is agreed among mariners to make the change of date at 
the 180th meridian from Greenwich. Ships crossing this line 
from the east skip one day in so doing. If it is Monday after- 
noon when a ship reaches the line, it becomes Tuesday after- 
noon the moment she passes it, the intervening 24 hours being 
dropped from the reckoning on the log-book. Vice versa, 
when a vessel crosses the line from the tvestern side, it counts 
the same day twice, passing from Tuesday back to Monday and 
having to do Tuesday over again. 

This 180th meridian passes mainly over the ocean, hardly touching 
land anywhere. There is some irregularity in the date actually used 
on the different islands in the Pacific. Those which received their 
earliest European inhabitants via the Cape of Good Hope, have, for 
the most part, adopted the Asiatic date, even if they really lie east of 
the 180th meridian, while those that were first approached via Cape 
Horn have the American date. When Alaska was transferred from 
Russia to the United States, it was necessary to drop one day of the 
week from the official dates. 

PLACE OE A SHIP AT SEA. 

67. The determination of the place of a ship at sea is the 
problem to which Astronomy mainly owes its economic im- 
portance. As was said a few pages back, national observa- 
tories and nautical almanacs were established in order to sup- 
ply the mariner with the data needed to make this determi- 
nation accurately and promptly. The methods employed are 
necessarily such that the required observations can be made 
with the sextant and chronometer. Fixed instruments (like the 
transit instrument and meridian circle) are obviously out of 
the question on board of a vessel. 



42 LATITUDE AND LONGITUDE AT SEA. C§ 68 

68. Latitude at Sea. — This is obtained by observing with 
the sextant the sun's maximum altitude, which, of course, is 
reached when the sun is crossing the meridian. Since at sea, 
the sailor seldom knows beforehand the precise chronometer 
time of local noon, the observer takes care not to be too late 
and begins to measure the sun's altitude a little before noon, 
repeating his observations every minute or two. At first the 
altitude will keep increasing, but when noon is reached the 
altitude will become stationary, and then begin to decrease. 
The observer uses, therefore, the maximum altitude obtained, 
which, duly corrected for " semi-diameter," " dip of the hori- 
zon/' " refraction," and " parallax," (see Appendix, Art. 492), 
gives him the true altitude of the sun's centre, and taking this 
from 90° we get its zenith distance. Looking in the almanac, 
we find there the sun's declination given for Greenwich (or 
Washington) noon of every day, with the hourly change, so 
that we can easily deduce the exact declination at the moment 
of the observation. Then the observer's latitude comes out at 
once, because (Art. 51) the latitude of the observer equals the 
sun's zenith distance plus the sun's declination. It is easy in ' 
this way, with a good sextant, to get the latitude within about 
half a minute of arc (or, roughly, half a mile). 

69. Determination of the Local Time and Longitude at Sea. 

— The usual method now employed for the longitude depends 
upon the chronometer. This is carefully " rated " in port ; that 
is, its error and its daily gain or loss are determined by com- 
parisons with an accurate clock for a week or two, the clock 
itself being kept correct by transit observations. By merely 
allowing for its gain or loss since leaving port and adding 
this gain or loss to the error which the chronometer had when 
brought on board, the seaman at once obtains the error of the 
chronometer on Greenwich time at any moment ; and allowing 
for this error, he has the Greenwich time itself with an accu- 
racy which depends only on the constancy of the chronometer's 



§ 69] THE POSITION OF A HEAVENLY BODY. 43 

rate : it makes no difference whether it is gaining much or 
little, provided its daily rate is always the same. 

He must also determine his own local time, and it must be 
done with the sextant, since, as was said before, an instrument 
like the transit cannot be used at sea. He does it by meas- 
uring the altitude of the sun, not at or near noon, as generally 
supposed, but when the sun is as near east or west as the cir- 
cumstances permit. From such an observation the sun's hour- 
angle, i.e., the apparent time (and from this the mean time), 
is easily found, by means of the so-called PZS triangle, pro- 
vided the ship's latitude is known (see Appendix, Art. 493). 
The longitude follows at once, being simply the difference be- 
tween the Greenwich time and the local time (Art. 63). 

For " Sumner's method " of determining a ship's place, see " Gen- 
eral Astronomy." 



Cf 



DETERMINATION OF THE POSITION OF A HEAVENLY 

BODY. 

As the basis of all our investigations in regard to the mo- 
tions of the heavenly bodies, we require a knowledge of their 
" places " in the sky at known times. The "place," so-called, 
is denned by the body's right ascension and declination. 

70. 1. By the Meridian Circle. — If a body is bright enough 
to be seen by the telescope of the meridian circle and comes to 
the meridian in the night time, its right ascension and declina- 
tion are best determined by that instrument. If the meridian 
circle is in exact adjustment, the right ascension of the object 
is simply the sidereal time when it crosses the middle wire of 
the reticle of the instrument. 

The "circle-reading," on the other hand, corrected for re- 
fraction and parallax, gives the polar distance of the object 
(the complement of its declination) if the "polar point" of 
the circle has been determined (see Appendix, Art. 549). A 
single complete observation with the meridian circle deter- 



44 THE POSITION OF A HEAVENLY BODY. [§ 70 

mines therefore both the right ascension and the declination 
of the object. 

71. 2. By the Equatorial. — If the body, a comet for instance, 
is too faint to be observed by the telescope of the meridian 
circle, which is seldom very powerful, or if it comes to the 
meridian only in the daytime, we usually accomplish our object 
by using the equatorial, and determine the position of the body 
by measuring the difference of right ascension and declination 
between it and some neighboring star, the place of which is 
given in a star-catalogue. 

In measuring this difference of right ascension and declination, we 
usually employ a " micrometer " (Art. 542), attached to the telescope. 
The difference of right ascension between the star and the object to be 
determined is measured by simply observing with the chronograph 
the transits of the two objects across wires that are placed north and 
south ; the difference of declination, by bisecting each object with 
one of the micrometer wires as it crosses the middle of the field of 
view. The observed differences must be corrected for refraction, 
and also for the motion of the body, if it is appreciable. 

In some cases " altitude and azimuth instruments," so-called, are 
used for such "extra-meridian" observations, especially in observing 
the moon. 

Art. 71*. Variation of Latitude. It has been discovered since 
1889 that latitudes on the earth's surface certainly undergo slight 
periodical changes, amounting sometimes to 0."6 within a year. In 
other words, the earth's poles are not absolutely fixed, but wander about 
to the extent of 50 or 60 feet, never going more than 30 feet or so 
from their mean position. The motion is found to be compounded 
of two : one circular with a period of exactly a year, the other in 
an elongated oval with a period of about 14 months. It is supposed 
to be due chiefly to causes depending upon the seasons, but the ex- 
planation is not yet complete. 

There is so far no evidence that any considerable changes have ever 
occurred in the position of the poles. 



§ 721 THE EARTH'S FORM, ETC. 45 



CHAPTER III. 

THE EARTH: ITS FORM, ROTATION, AND DIMENSIONS. -- 

MASS, WEIGHT, AND GRAVITATION. THE EARTH'S 

MASS AND DENSITY. 

72. In a science which deals with the heavenly bodies it 
might seem at first that the earth has no place ; but certain 
facts relating to it are just such as we have to investigate with 
respect to her sister planets, are ascertained by astronomical 
methods, and a knowledge of them is essential as a base of 
operations. In fact, Astronomy, like charity, "begins at home," 
and it is impossible to go far in the study of the bodies which 
are strictly " heavenly" until one has first acquired some 
accurate knowledge of the dimensions and motions of the 
earth itself. 

73. The astronomical facts relating to the earth are broadly 
these : 

1. The earth is a great ball about 7920 miles in diameter. 

2. It rotates on its axis once in twenty-four sidereal hours. 

3. It is not exactly spherical, but is flattened at the poles, the 
polar diameter being nearly twenty-seven miles, or about one tivo 
hundred and ninety-fifth part, less than the equatorial. 

4. It has a mean density between 5.5 and 5.6 as great as 
that of icater, and a mass represented in tons by six ivith twenty- 
one ciphers following {six thousand millions of millions of millions 
of tons). 

5. It is flying through space in its orbited motion around the 
sun with a velocity of about eighteen and a half miles a second ; 
i.e., about seventy-five times as swiftly as an ordinary cannon- 
ball 



46 SIZE OF THE EARTH. [§ 74 



74. The Earth's Approximate Form and Size. — It is not 

necessary to dwell on the ordinary proofs of the earth's globu- 
larity. We will simply mention them. 

1. It can be circumnavigated. 

2 t The appearance of vessels coming in from sea indicates 
that the surface is everywhere convex. 

3. The fact that the dip of the sea horizon (Art. 16) , as 
seen from a given elevation, is (sensibly) the same in all direc- 
tions, and at all parts of the earth, shows that the surface is 
approximately spherical. 

4. The fact that as one goes from the equator towards the 
north the elevation of the pole increases in proportion to the 
distance from the equator proves the same thing. 

5. The outline of the earth 1 's shadoio, seen upon the moon dur- 
ing lunar eclipses, is such as only a sphere could cast. 

We may add, as to the smoothness and roundness of the 
earth, that if the earth be represented by an 18-inch globe, 
the difference between its greatest and least diameters would 
be only about one-sixteenth of an inch ; the highest mountains 
would project only about one-ninetieth of an inch, and the 
average elevation of continents and depths of the ocean would 
be hardly greater on that scale than the thickness of a film of 
varnish. Relatively, the earth is really much smoother and 
rounder than most of the balls in a bowling alley. 

75. The Approximate Measure of the Earth's Diameter. — 

There are various ways of determining the diameter of the 
earth. The best, in fact the only accurate one, is by measur- 
ing arcs of meridian, so as to ascertain the number of miles or 
kilometres in a degree of the earth's circumference. This will 
be more fully discussed in Articles 86-89. 

There are various approximate methods, one of the simplest 
of which is the following : 

Erect upon a reasonably level plane three rods in line, a mile 



$76] 



THE EARTH'S DIAMETER AND ROTATION. 



47 



apart from eacli other, and cut off their tops at the same levei, 
carefully determined with a surveyor's levelling instrument. 
It will then be found, on sighting across from A to C (Fig. 15), 
that the line, after allowing for refraction, passes about eight 
inches below B, the top of the middle rod. 

Suppose the circle ABC completed, and that E is the point of 
the circumference opposite B, so that BE equals the diameter 
of the earth (i.e., BE = 2BJ. By geometry, 



BD:BA::BA:BE; whence BE = 



BA 2 




Fig. 15. — Curvature of the Earth's Surface. 

Now BA is one mile, and BD equals two-thirds of a foot, or 
YW21J of a mile; hence BE equals 

[2 ■ = 7920 miles. 



i 

7920 

On account of refraction, however, the result cannot be made exact. 
The necessary correction is large, and varies with the thermometer 
and barometer ; so that the actual observed length of BD, instead of 
being 8 inches, ranges from 5 to 7 according to circumstances. 

EL 

76. The Rotation of the Earth. — At the time of Copernicus 
the only argument he could adduce in favor of the earth's 
rotation 1 was that the hypothesis is much more probable than 
the older one, that the heavens themselves revolve. 

1 The word "rotate" denotes a spinning motion like that of a wheel on 
its axis. The word "revolve" is more general, and may be applied either 
to describe such a spinning motion, or (and this is the more usual use in 
Astronomy), to describe the motion of a body travelling around another, 
as when we say that the earth " revolves " around the sun. 



48 



FOUCAULT S PENDULUM EXPERIMENT. 



[§76 



All the phenomena then known would be sensibly the same 
on either supposition. The apparent diurnal motion of the 
heavenly bodies can be fully accounted for (within the limits 
of the observations then possible) either by supposing that the 
stars are actually attached to a celestial sphere which turns 
daily, or that the earth itself rotates upon an axis ; and for a 
long time the latter hypothesis did not seem to most people 
so probable as the older and more obvious one. 

A little later, after the telescope had been invented, analogy 
could be adduced ; for with the telescope we can see that the 

sun, moon, and many of the 
planets are rotating globes. 
Within the present century 
it has become possible to 
adduce experimental proofs 
which go still further, and 
absolutely demonstrate the 
earth's rotation : some of 
them even make it visible. 

77. Foucault's Pendulum 
Experiment. — Among these 
experimental proofs the most 
impressive is the pendulum 
experiment devised and first 
executed by Foucault in 1851. 
From the dome of the Pan- 
theon in Paris, he hung a 
heavy iron ball about a foot 
in diameter by a wire more 
than 200 feet long (Fig. 16). A circular rail some twelve 
feet across, with a little ridge of sand built upon it, was placed 
in such a way that a pin attached to the swinging ball would 
just scrape the sand and leave a mark at each vibration. To 
put the ball in motion it was drawn aside by a cotton cord and 




Fig. 16. — Foucault's Pendulum Experiment. 



§ 77] INVARIABILITY OF THE EARTH'S ROTATION. 49 

left to come absolutely to rest ; then the cord was burned off, 
and the pendulum started to swing in a true plane. But this 
plane seemed to deviate slowly towards the right, so that the pin 
on the pendulum-ball cut the sand-ridge in a new place at 
each swing, shifting at a rate which would carry the line com- 
pletely around in about 32 hours, if the pendulum did not first 
come to rest. In fact the floor of the Pantheon was actually 
and visibly turning under the plane of the pendulum vibra- 
tion. The experiment created great enthusiasm at the time, 
and has since been frequently performed. 

For fuller discussion, see Appendix, Art. 494. 



78. We merely mention (without discussion) a number of other 
demonstrations of the earth's rotation. 

(a) By the gyroscope, an experiment also due to Foucault. 

(b) The slight eastward deviation of bodies in falling from a great 
height. The idea of the experiment was first suggested by Xewton, 
but its actual execution has only been carried out during the present 
century — by several different observers. 

(c) The deviation of projectiles. 

(d) Various phenomena connected with Meteorology and Physical 
Geography, such as the direction of the trade winds and the great 
currents of the ocean, wmich are determined by the earth's rotation ; 
so also the direction of the revolution of cyclones, which in the north- 
ern hemisphere move contrary to the hands of a w 7 atch, while in 
the southern their motion is in the opposite direction (see "General 
Astronomy"). 

It might seem at first that the rotation of the earth in 24 
hours is not a very rapid motion. A point on the equator 
moves, however, nearly 1000 miles an hour, which is about 1500 
feet per second, — very nearly the speed of a cannon-ball. 

79. Invariability of the Earth's Rotation. — It is a question 
of great importance whether the day ever changes its length. 
Theoretically, it must almost necessarily do so. The friction 
of the tides and the deposit of meteoric matter upon the earth 



50 THE EARTH'S ROTATION. [§ 79 

both tend to retard the earth's rotation ; while, on the other 
hand, the earth's loss of heat by radiation and the consequent 
shrinkage must tend to accelerate it and to shorten the day. 
Then geological causes act some one way and some the other. 
At present we can only say that the change, if any change 
has occurred since Astronomy became accurate, has been too 
small to be detected. 

The day is certainly not longer or shorter by the T ^$ part of a second 
than it was in the days of Ptolemy ; probably it has not changed by 
the j^oo part. The criterion is found in comparing the times at 
which celestial phenomena, such as eclipses, transits of Mercury, etc., 
have occurred during the range of astronomical history. Professor 
Xewcomb's investigations in this line make it highly probable, how- 
ever, that the length of the day has not been absolutely constant dur- 
ing the last 150 years. 

80. Effects of the Earth's Rotation upon Gravity on the 
Earth's Surface. — As the earth rotates, every particle of its 
matter is subjected to a so-called "centrifugal force" directed 
away from the axis of the earth (Physics, page 73), and this 
force depends upon the radius of the circle upon which the 
particle moves, and the velocity with which it moves. 

yi 

The formula is C=-^-, in which V is the velocity of the moving 

particle, R the radius of the circle, and C is the centrifugal force, 
expressed as an" acceleration" in the same way that gravity is expressed 
by (7, — the velocity of 32 \ feet, which a falling body acquires in the 
first second of its fall. 

As stated in the Physics in the passage referred to, a body 
at the equator of the earth has its weight diminished by yi-g- part, 
in consequence of this force. (But see Art. 91.) 

81. Effect of Centrifugal Force in diminishing Gravity. — 

Between the equator and the poles the centrifugal force is 
less than at the equator, because the circle described each day 
by a body at the earth's surface is smaller, its distance from 




§ 81] CENTRIFUGAL FORCE. 51 

the axis being less. Moreover, as shown in Fig. 17, the cen- 
trifugal force MT at M, since it acts at right angles to the 
earth's axis, OP, is not directly op- 
posed to the earth's attraction, which 
acts (nearly) on the line MO ; it is 
not, therefore, wholly effective in 
diminishing the weight of the body. 
To ascertain the effect produced 
upon the weight, MT must be " re- 
solved" (Physics, p. 91) into the 
two component forces MR and MS. 

The first of these alone acts to les- The Earth > 8 Centrifugal Force. 

sen the weight. 

82. Effect of the Horizontal Component of the Centrifugal 
Force. — The horizontal component MS tends to make the 
plumb-line deviate from the line MO (drawn to the earth's 
centre) towards the equator, so as to make a smaller angle 
with the earth's axis than it otherwise would. 

In latitude -15°, this horizontal component of the centrifugal force 
has a maximum equal to about ^Ij of the whole force of gravity, and 
causes the plumb-line to deviate about 11' from the direction it would 
otherwise take. 

If the earth's surface were strictly spherical, this horizontal force 
would make every loose particle tend to slide towards the equator, 
and the water of the ocean would so move. As things are, the sur- 
face has arranged itself accordingly, and the earth bulges at the 
equator just enough to counteract this sliding tendency. 

83. Gravity. — What is technically called "gravity" is not 
simply the attraction of the earth for a body upon its surface, 
but the resultant of the attraction combined ivith this centrifugal 
force. It is only at the equator and at the pole that " gravity " 
is directed strictly towards the earth's centre. Lines of level 
are always perpendicular to " gravity," and they are, therefore, 
not true circles around the earth's centre. If the earth's rota- 



52 THE earth's DIMENSIONS. [§ 83 

tion were to cease, the Mississippi River would at once have 
its course reversed, since the mouth of the river is several 
thousand feet further from the centre of the earth than are 
its sources. 

84. Accurate Determination of the Earth's Dimensions. — 

The form of the earth, instead of being spherical, is much 
more nearly that of an " oblate spheroid of revolution " (an 
orange-shaped solid) quite sensibly flattened at the poles ; the 
polar diameter being shorter than the equatorial by about ^j 
part. According to " Clarke's l Spheroid of 1866 " (which is 
adopted by our Coast and Geodetic Survey as the basis of all 
calculations) the dimensions of the earth are as follows : — 

Equatorial radius, (a) 6,378,206.4 metres = 3963.307 miles. 
Polar radius, (6) 6,356,583.8 metres = 3949.871 " 

Difference, 21,622.6 metres = 13.436 " 

These numbers are likely to be in error as much, perhaps, as 100 
metres, and possibly somewhat more ; they can hardly be 300 metres 
wrong. 

This deviation of the earth's form from a true sphere is due 
simply to its rotation, and might have been cited as proving 
it. The centrifugal force caused by the rotation modifies the 
direction of gravity everywhere except at the equator and 
the poles (Art. 82) ; and so the surface necessarily takes the 
spheroidal form. 

85. Methods of Determining the Earth's Form. — There are 
several ways of doing this : one by measurement of distances upon 
its surface in connection with the latitudes and longitudes of 
the points of observation. This gives not only the form, but 
the dimensions also ; i.e., the size in miles or metres. An- 

1 Col. A. R. Clarke, now for many years at the head of the English Ord- 
nance Survey. 



§ 85] MEASUREMENT OF AN AKC. 53 

other method is by the observation of the force of gravity at 
various points — observations which are made by means of a 
pendulum apparatus of some kind, and determine only the 
form of the earth, but not its size. 

86. The simplest form of the method by actual measure- 
ment is that in which we determine the length of degrees of 
latitude, some near the equator, and others near the poles, 
and still others intermediate. 

If the earth were exactly spherical, the length of a degree 
would, of course, be everywhere the same. Since it is not, the 
length of a degree will be greatest where the earth is most 
nearly flat ; i.e., near the poles; in other words, the distance 
between two points on the same meridian having their plumb- 
lines inclined to each other at an angle of one degree will be 
greatest where the surface is least curved. 

The measurement of an " arc " involves two distinct sets of 
operations, one purely astronomical, the other geodetic. Hav- 
ing selected two terminal stations several hundred miles apart, 
and one of them as nearly as possible due north of the other, 
we must determine first the distance between them in feet or 
metres, and second (by astronomical observations), their differ- 
ence of latitude in degrees, with the exact azimuth or bearing of 
the line that connects them. 

87. Geodetic Operations. — The determination of the distance 
in feet or metres. It is not practicable to measure this with 
sufficient accuracy directly, as by simple " chaining," but we 
must have recourse to the process known as " triangulation." 

Between the two terminal stations (A and H, Fig. 18) others are 
selected such that the lines joining them form a complete chain of 
triangles, each station being visible from at least two others. The 
angles at each station are carefully measured; and the length of one 
of the sides, called the " base" is also measured with all possible pre- 
cision. It can be done with an error not exceeding an inch in ten 



54 



LENGTH OF A DEGKEE. 



[§87 



miles. (BU is the base in the figure.) Having the length of 
the base, and all the angles, it is then possible to calculate every 
other line in the chain of triangles. An error of more than three 
feet in a hundred miles would be unpar- 
donable. 

88. Astronomical Operations. — By as- 
tronomical observations we must deter- 
mine (a) the true bearing or azimuth of 
the lines of the triangulation, and also (b) 
the difference of latitude in degrees be- 
tween A and H. 

To effect the first object, it will be suffi- 
cient to determine the azimuth of any one 
of the sides of the system of triangles by the 
method given in the Appendix, Art. 495. 
This being known, the azimuth of every 
other line is easily got from the measured 
angles, and we can then compute how many 
feet or metres one terminal station is north 
of the other, — the line Ah in the figure. 

(b) The difference of latitude. This is 
obtained simply by determining the latitudes 
of A and // by one of the methods of Art. 47, 
or by any other method that will determine 
astronomical ]atitudes with precision. It is 
well, also, to measure the latitudes of a num- 
ber of the intermediate stations, and to determine the azimuths of a 
number of lines of the triangulation instead of a single one (in order 
to lessen the effect of errors of observation) . 

89. The Length of a Degree of Latitude. — The geodetic and 
astronomical observations thus give the length of the line Ah, 
both in feet and in degrees, so that Ave immediately find the 
number of feet in that degree of latitude which has its middle 
point half-way betiveen A and h. If the earth were spherical, 
the length of a degree would be everywhere the same, and the 




Fig. 18. 






§ 89] THE ELLIPTICITY OF THE EARTH. 55 

earth's diameter would be found simply by multiplying the 
length of one degree by 360 and dividing the product by ir, 
that is, 3.1415926. 

More than twenty such arcs have been measured in differ- 
ent parts of the world, varying in length from 25° to 2°, and 
it appears clearly that the length of the degrees, instead of 
being everywhere the same, increases toivards the 'pole. 

At the equator, one degree = 68.701 miles 



At lat. 20° 


a 


" = 68.786 


a a £QO 


« 


" = 68.993 


" " 60° 


a 


^ = 69.230 


" " 80° 


a 


" = 69.386 


At the pole, 


" 


" = 69.407 



The difference between the equatorial and polar degree of 
latitude is more than seven-tenths of a mile, or over 3500 feet ; 
while the probable error of measurement cannot exceed a foot 
or two to the degree. 



90. The Ellipticity or Oblateness of the Earth. — The cal- 
culations by which the precise form of the earth is deduced 
from such a series of measurements of arcs lie beyond our 
scope, but the net result is as stated in Art. 84. 

The fraction obtained by dividing the difference between the 
equatorial and polar radii, by the equatorial {i.e., the frac- 
tion — ^-), is called by various names, such as the "Polar 

Comjjression" the "Ellipticity" 1 or the Oblatexess, of the 
earth ; the last term being most used. 

Owing to the obvious irregularities in the form of the earth, 
the results obtained by combining the arcs in different ways 



1 This "ellipticity" of the earth's elliptical meridian must not he con- 
founded with its "eccentricity" the formula for which is -vL 



J a ' 2 - b '\ The 



" ellipticity " of the earth's meridian is about Y iy> its "eccentricity" 
nearly y 1 ^. 



56 DETERMINATION OF THE EARTH'S FORM. [§ 90 

are not exactly accordant, so that a very considerable vari- 
ation is found in the ellipticity as deduced by different 
authorities. 

91. Determination of the Earth's Form by Pendulum Experi- 
ments. — For details of experiments of this kind we must 
refer the reader to the " General Astronomy ." It is sufficient 
for our purpose simply to say that such observations show 
that the force of gravity is greater at the pole than at the equator 
by about T ^ part; i.e., weighed in a spring balance, a man who 
weighs 190 pounds at the equator would weigh 191 at the 
pole. The centrifugal force of the earth's rotation accounts 
for about one pound in 289 of the difference. The remainder 
(about one pound in 555) has to be accounted for by the differ- 
ence between the distances of the centre of the earth from the 
pole and from the equator. At the pole a body is nearer the 
centre of the earth than anywhere else on the earth's surface, 
and as a consequence the earth's attraction upon it is greater. 

The result of the pendulum observations thus far made indicates 
for the earth an ellipticity of about ^^, — in practical (though not 
absolute) agreement with the result derived by measurement of arcs. 

There are other purely astronomical methods of determining the 
form of the earth, depending upon certain irregularities in the moon's 
motion which are due to the "bulge " at the earth's equator ; and upon 
the moon's effect in producing "precession " (Art. 124). They indi- 
cate a slightly smaller "oblateness" of about ;,} U) . 

92. Station Errors. — If the latitudes of all the stations in a tri- 
angulation, as determined by astronomical observations, are compared 
with their differences of latitude as deduced from trigonometrical 
operations, we find the discrepancies by no means insensible. They 
are in the main due not to errors of observation, but to irregularities 
in the direction of (/rarity, and depend upon the variations in the density 
of the crust and the irregularities of the earth's surface. Such irregular- 
ities are called station errors. According to the Coast Survey, in the 



§92] ASTRONOMICAL AND GEOGRAPHICAL LATITUDE. 57 

eastern part of the United States these station errors average about 
1J seconds of arc, affecting both the longitudes and latitudes of the 
stations, as well as the astronomical azimuths of the lines that join 
them. Station errors of from 4" to G" are not very uncommon, and 
in mountainous countries these deviations occasionally amount to 30" 
or 40". 

93. Distinction between Astronomical and Geographical Lat- 
itude. — The astronomical latitude of the station is that actually deter- 
mined by astronomical observations. The geographical latitude is the 
astronomical latitude corrected for "station error' 1 It may be defined 
as the angle formed with the plane of the equator by a line drawn 
from the place perpendicular to the surface of the "standard spheroid" 
at that station. Its determination involves the adjustment and even- 
ing-off of the discrepancies between the geodetic and astronomical 
results over extensive regions of country. The geographical latitudes 
are those used in constructing a map. 

For most purposes, however, the distinction may be neglected, 
since on the scale of an ordinary map the " station errors " would 
be insensible. 

94. Geocentric Latitude. — The astronomical latitude at any 
place (Art. 47) is, it will be remembered, the angle between 
the plane of the equator and the direction of gravity at that 
place. The geocentric latitude, on the other hand, is the angle 
made at the centre of the earth, as the word implies, between 
the plane of the equator and a line drawn from the observer 
to the centre of the earth; which line, evidently does not coin- 
cide with the direction of gravity, since the earth is not 

spherical. 

• 

In Fig. 19, the angle MNQ is the astronomical latitude of the point 
M. (It is also the geographical latitude, provided the " station error" 
at that point is insensible.) The angle MOQ is the geocentric lati- 
tude. 

The angle ZMZ', which is the difference of the two latitudes, is 
called the angle of the vertical. 



58 



SURFACE AND VOLUME OF THE EARTH. 



[§94 



The geocentric degrees are longer near the 
equator than near the poles, and it is worth 
noticing that if we form a table like that 
of Art. 89, giving the length of each degree 
of geographical latitude from the equator 
to the pole, the same table, read backwards, 
gives the length of the geocentric degrees ; 
i.e., at the pole a degree of geocentric lati- 
jV ~q tude is 68.704 miles, and at the equator 

Fig. 19. — Astronomical and ^9 .407 miles. 

Geocentric Latitude. Geocentric latitude is seldom employed 

except in certain astronomical calculations 
in which it is necessary to " reduce the observations to the centre of 
the earth. " 




95. Surface and Volume of the Earth. — The earth is so 
nearly spherical that we can compute its surface and volume with suf- 
ficient accuracy by the formulae for a perfect sphere, provided we put 
the earth's mean semi-diameter for r in the formulae. This mean semi- 
diameter of an oblate spheroid is not , but — ^ — , because if we 

draw through the earth's centre three axes of symmetry at right 
angles to each other, one will be the axis of rotation and both the 
others will be equatorial diameters. The mean semi-diameter r of the 
earth thus computed is 3958.83 miles ; its surface (47rr 2 ) is 196,944,000 
square miles, and its volume (f irr z ), 260,000 million cubic miles, in 
round numbers. 



III. 

THE EAKTH'S MASS AND DENSITY. 

96. Definition of Mass. — The mass of a body is the " quan- 
tity of matter" in it; i.e., the number of " pounds," "kilo- 
grams," or "tons" of material it contains. It must not be 
confounded with the " volume " of a body, which is simply its 
bulk ; i.e., the number of cubic feet or cubic miles in it ; nor is 
it identical with its " weight" which is simply the force with 
which the body tends to move towards the earth. It is true 
that under ordinary circumstances the mass of a body and its 



§ 96] THE EARTH'S MASS AND DENSITY. 59 

weight are proportional, and numerically equal ; a mass of ten 
pounds " weighs " very nearly ten pounds under ordinary cir- 
cumstances ; but the word " pound " in the two halves of the 
sentence means two entirely different things; the pound of 
"mass" is one thing, the pound of "force" a very different one. 

97. Mass and Force distinguished. — This identity of names 
for the units of mass and force leads to perpetual ambiguity, 
and is very unfortunate, though the reason for it is per- 
fectly obvious, because in most cases we measure masses by 
weighing. The unit of mass is a certain piece of platinum, or 
some such unalterable substance which is kept at the national 
capital, and called the standard "pound," or "'kilogram." The 
pound or kilogram of weight or force, on the other hand, is 
not the piece of metal at all, but the attraction between it and 
the earth at some given place, as, for instance, Paris. It is a 
pull or a stress. 

The mass of a given body, — the number of mass-pounds in 
it — is invariable ; its iveight, on the other hand, — the number 
of /orce-pounds which measures its tendency to fall, — depends 
on where the body is. At the equator it is less than at the 
pole ; at the centre of the earth it would be zero, and on the 
surface of the moon only about one-sixth of what it is on 
the earth's surface. 

The student must always be on his guard whenever he 
comes to the word "pound" or any of its congeners, and 
consider whether he is dealing with a pound of mass or force. 

Many high authorities now advocate the entire abandonment of 
these old force-units which bear the same names as the mass-units, 
and the substitution in all scientific work of the dyne (Physics, p. 40) 
and its derivative, the megadyne. The change would certainly con- 
duce to clearness, but would, for a time at least, involve much incon- 
venience. The dyne equals ™tu~5-' or 1-0199, times the iceight of a 
milligramme at Paris; and the megadyne, 1.0199 times the weight of 
a kilogramme at the same place. 



60 the measuremp:nt of MASS. [§ 98 

98. The Measurement of Mass. — This is usually effected by 
a process of " weighing " with some kind of balance, by means 
of which we ascertain directly that the " weight " of the body 
is the same as the weight of a certain number of the standard 
units in the same place, and thence infer that its mass is the 
same. 

It may be done also, though in practice not very conveniently, by 
ascertaining what velocity is imparted to a body by the expenditure 
of a known amount of energy (see Appendix, Art. 496). 

But it is obvious that neither of these methods could be 
used to measure the enormous mass of the earth, and we must 
look for some different process by which to ascertain the num- 
ber of tons of matter it contains. 

The end is accomplished by comparing the attraction which 
the earth exerts upon some body at its surface, with the attrac- 
tion exerted upon the same body by a knoivn mass at a known 
distance. 

99. Gravitation. The Cause of "Weight." — Science cannot 
yet explain why bodies tend to fall towards the earth, and push 
or pull towards it when held from moving. But Newton dis- 
covered that the phenomenon is only a special case of the much 
more general fact which he inferred from the motions of the 
heavenly bodies, and formulated as " the laic of gravitation" l 
under the statement that any tivo particles of matter " attract " 
each other with a force which is proportioned to their masses and 
inversely proportioned to the square of the distance between them. 

If instead of particles we have bodies composed of many 
particles, the total force between the bodies is the sum of the 
attractions of the different particles, each particle attracting 
every particle in the other body. 



1 The word " gravitation" is used to denote the attraction of bodies for 
each other in general, while "gravity" (French u pesanteur") is limited to 
the force which makes bodies fall at the surface of the earth or other heavenly body. 






§ 100] THE ATTRACTION OF SPHERES. 61 

100. We must not imagine the word " attract " to mean too 
much. It merely states as a fact that there is a tendency for 
bodies to move toward each other, ivithout including or imply- 
ing any explanation of the fact. 

Thus far no explanation has appeared which is less difficult to com- 
prehend than the fact itself. Whether bodies are drawn together by 
some outside action, or pushed together, or whether they themselves 
can "act " across space with mathematical intelligence, — in what way 
it is that "attraction " comes about, is still unknown, and apparently 
as inscrutable as the very nature and constitution of an atom of mat- 
ter itself. It is at present simply a fundamental fact, though it is not 
impossible that ultimately we may be able to show that it is a neces- 
sary consequence of the relation between particles of ordinary matter 
and the all-pervading " ether " to which we refer the phenomena of 
light, radiant heat, electricity, and magnetism (Physics, p. 315). 

101. The Attraction of Spheres. — If the two attracting 
bodies are spheres, either homogeneous, or made up of concen- 
tric shells which are of equal density throughout, Newton 
showed that the action is precisely the same as if all the matter 
of each sphere were collected at its centre ; and if the distance 
between the bodies is very great compared ivith their size, then, 
whatever their form, the same thing is very nearly true. 

If the bodies are prevented from moving, the effect of at- 
traction will be a stress or pull, to be measured in dynes or 
/orce-units (not mass-units), and is given by the equation 

F (dynes) = GXM l X M 2 -r el 2 , 

where M x and 3I 2 are the masses of the two bodies expressed in 
mass-units (grammes), d is the distance between their centres 
(in centimetres), and G is a factor known as "The Constant of 
Gravitation," which equals 0.0000000666 according to the latest 
determination by Boys in 1894. G will of course have a differ- 
ent numerical value if other units of mass and distance are used. 1 

1 It will not do to write the formula F= ? X * (omitting the £), un- 

d 2 
less the units are so chosen that the unit of force shall be equal to the 



y 



62 



ACCELERATION BY GRAVITATION. 



[§ 102 



102. Acceleration by Gravitation. — If M x and M 2 are set free 
while under each other's attraction, they will at once begin to approach 
each other, and will finally meet at their common centre of gravity, 
having moved all the time with equal "momenta" (Physics, p. 115), 
but with velocities inversely proportional to their masses. At the end of 
the first second M x will have acquired a velocity of 

«■*§• 

which, the student will observe, is entirely independent of M x itself : 
a grain of sand and a heavy rock fall at the same rate in free space 
under the attraction of the same body, at the same distance from it. 
(In the C. G. S. system G 1 is identical with G. In other systems of 
units it is usually numerically different.) 
acquired a velocity 



Similarly M 2 will have 



G*X 



d 2 ' 



/=*(*$*)• 



This is the form of the law of gravitation which is most used in deal- 
ing with the motions of the heavenly bodies. The reader will notice 
that while the expression for F (the force in dynes) has the product of 
the masses in its numerator, that for f (the acceleration) has their 
sum. 



103. We are now prepared to discuss the methods of meas- 

It is only necessary, as has been 



uring the earth's mass 



The velocities with which the two bodies are approaching each other 
will be the sum of these velocities ; and if we denote this " accelera- 
tion " (or the velocity of approach acquired in one second) by f, just 
as g is used to denote the acceleration due to gravity in a second, we 
shall have 



attraction between two masses each of one unit at a distance of one unit. 
It is not true that the attraction between two particles, each having a mass 
of one pound, at a distance of one foot, is equal to a stress of either one 
pound or one dyne. 



§ 103J THE TORSION BALANCE. 63 

already said (Art. 98), to compare the attraction which the 
earth exerts on a body, X at its surface (at a distance, 
therefore, of 3959 miles from its centre) with the attraction 
exerted upon X by some other body of a known mass at a 
known distance. The practical difficulty is that the attrac- 
tion of any manageable body is so very small, compared with 
that of the earth, that the experiments are extremely delicate, 
and unless the mass is one of several tons, its attraction will 
be only a minute fraction of a grain of force, hard to detect 
and worse to measure. 

The different methods which have been actually used for determin- 
ing the mass of the earth are enumerated and discussed in the " Gen- 
eral Astronomy," to which the student is referred. We limit ourselves 
to the presentation of a single one, which is perhaps the best, and is 
not difficult to understand. 

104. The Earth's Mass and Density determined by the 
Torsion Balance. — This is an apparatus invented by Michell, 
but first employed by Cavendish, in 1798. A light rod 
carrying two small balls at its extremities is suspended 
at its centre by a fine, metallic wire, so that it will hang 
horizontally. If it be allowed to come to rest, and then a 
very slight deflecting force be applied, the rod will be pulled 
out of position by an amount depending on the stiffness 
and length of the wire as well as the intensity of the force. 
Wliea the deflecting force is removed, the rod will vibrate 
back and forth until brought to rest by the resistance of 
the air. The " torsional coefficient" as it is called, i.e., the 
stress which will produce a twist of one revolution, can be 
accurately determined by observing the time of vibration, when 
the dimensions and weight of the rod and balls are known. 
(See Physics (Anthony & Brackett), p. 117.) This will 
enable us to determine what fraction of a grain (of force) or 
of a dyne is necessary to produce a twist of any number of 
degrees. 



64 



CALCULATION OF THE EARTHS MASS. 



[§105 



105. If, now, two large balls, A and B, Fig. 20, are brought 
near the smaller ones, as shown in the figure, a deflection will 
be produced by their attraction, and the small balls will move 
from a and b to a' and b'. By shifting the large balls to the 
other side at A' and B' (which can be done by turning the 
frame upon which these balls are supported) we get an equal 

deflection in the opposite direc- 
tion ; that is, from a f and b 1 to 
\ a" and b n , and the difference 
J between the two positions as- 
sumed by the two small balls, 
that is a! a" and b'b" will be twice 
the deflection. 




It is not necessary, nor even best, 
to wait for the balls to come to rest. 
When vibrating slightly we note the 
extremities of their swing. The mid- 
dle point of the swing gives the place 
of rest, while the time occupied by 
the swing is the period of vibration, 
which we need in determining the 
coefficient of torsion. We must also 
measure the distances A a', A'b", Bb', 
and B'a" between the centre of each 
of the large balls and the point of rest of the small ball when deflected. 



Fig. 20. — Plan of the Torsion Balance. 



106. Calculation of the Earth's Mass from the Experiment. 

— The earth's attraction on each of the small balls evidently 
equals the ball's weight. The attractive force of the large ball 
on the small one near it is found from the observed deflection. 
If, for instance, this deflection is 1°, and the coefficient of tor- 
sion is such that it takes one grain (of force) to twist the wire 
one whole turn, then the deflecting force, which we will call 
/, will be -gi-^ of a grain. One-half of this deflecting force will 
be due to A's attraction of a ; half, to i?'s attraction of b. Call 



§ 106] DENSITY OF THE EARTH. 65 

the mass of the large ball B and that of the small ball b, and 
let d be the measured distance Bb 1 between their centres. We 
shall then have the equation 

i/=GtlL£* or B = i & (1) 

Similarly calling E the mass of the earthy and R its radius, 
zv being the weight of the small ball (which weight measures 
the force of the earth's attraction upon it), we shall have 

whence (dividing the second equation by the first), 

i= 2 (?)(f) 

which gives the mass of the earth in terms of B. 

107. Density of the Earth. — Having the mass of the earth, 
it is easy to find its density. The volume or bulk of the earth 
in cubic miles has already been given (Art. 95), and can be 
found in cubic feet by simply multiplying that number by the 
cube of 5280. Since a cubic foot of water contains &2\ mass- 
pounds (nearly), the mass the earth would have, if composed 
of water, follows. Comparing this with the mass actually ob- 
tained, we get its density. A combination of the results of all 
the different methods hitherto employed, taking into account 
their relative accuracy, gives about 5.55 as the most probable 
value of the density of the earth according to our present 
knowledge. 

108. In the earlier experiments by this method, the small balls 
were of lead, about two inches in diameter, at the extremities of a light 
wooden rod five or six feet long enclosed in a case with glass ends ; 
and their position and vibration was observed by a telescope looking 



66 CONSTITUTION OF THE EARTH'S INTERIOR. [§ 108 

directly at them from a distance of several feefc. The attracting 
masses, A and B, were balls (also of lead) about one foot in diameter. 

Boys in 1894 used a most refined apparatus in which the small 
balls of gold, \ of an inch in diameter, were hung at the end of a 
beam only half an inch long which was suspended by a delicate fibre 
of quartz. The deflections due to the attraction of two sets of lead 
balls, respectively 2i and 4| inches in diameter, were measured by 
observing with a telescope the reflection of a scale in a little mirror 
attached to the beam. He obtained 5.527 for the earth's density. 
Earlier determinations by Cornu and Wilsing have given 5.56 and 
5.58 respectively. A still later important determination by a differ- 
ent method, completed by Richarz at Berlin in 1896, gives 5.505. 

From Equation (1) page 65, G — \fd 2 -r b X B ; so that it is de- 
terminable directly from the observations, without any reference to 
the density of the earth. 

109. Constitution of the Earth's Interior. — Since the average 
density of the earth's crust does not exceed three times that 
of water, while the mean density of the whole earth is about 
5.55, it is obvious that at the earth's centre the density must 
be very much greater than at the surface, — very likely as 
high as eight or ten times the density of water, and equal to 
that of the heavier metals. There is nothing surprising in 
this. If the earth were once fluid, it is natural to suppose 
that in the process of solidification the densest materials 
would settle towards the centre. 

Whether the centre of the earth is solid or fluid, it is difficult to 
say with certainty. Certain tidal phenomena, to be mentioned here- 
after, have led Lord Kelvin to express the opinion that the earth as a 
whole is solid throughout, and "more rigid than glass " volcanic cen- 
tres being mere "pustules," so to speak, in the general mass. To 
this most geologists demur, maintaining that at the depth of not 
many hundred miles the materials of the earth must be fluid or at 
least semi-fluid. This is inferred from the phenomena of volcanoes, 
and from the fact that the temperature continually increases with 
the depth so far as we have yet been able to penetrate. 






§ HOJ APPARENT MOTION OF THE SUN. 67 



CHAPTER IV. 

THE APPARENT MOTION OF TELE SUN, AND THE ORBITAL 
MOTION OF THE EARTH. — PRECESSION AND NUTATION. 
— ABERRATION. — THE EQUATION OF TIME. — THE SEA- 
SONS AND THE CALENDAR. 

. 110. The Sun's Apparent Motion among the Stars. — The 

sun has an apparent motion among the stars which makes it 
describe the circuit of the heavens once a year, and must have 
been among the earliest recognized of astronomical phenomena, 
as it is obviously one of the most important. 

As seen by us in the United States, the sun, starting in the 
spring, mounts higher in the sky each day at noon for three 
months, appears to stand still for a few days at the summer 
solstice, and then descends towards the south, reaching in 
the autumn the same -noon-day elevation which it had in the 
spring. It keeps on its southward course to the winter sol- 
stice in December, and then returns to its original height at 
the end of a year, marking and causing the seasons by its 
course. 

Nor is this all. The sun's motion is not merely a north and 
south motion, but it also advances continually eastward among 
the stars. In the spring the stars, which at sunset are rising 
in the eastern horizon, are different from those which are 
found there in summer or winter. In March the most con- 
spicuous of the eastern constellations at sunset ,are Leo and 
Bootes. A little later Virgo appears, in the summer Ophiuchus 
and Libra ; still later Scorpio, while in midwinter Orion and 
Taurus are ascending as the sun goes down. 



68 THE ECLIPTIC, r§ in 

111. So far as the obvious appearances are concerned, it is 
quite indifferent whether we suppose the earth to revolve 
arouncT the sun, or vice versa. That the earth really moves, 
is absolutely demonstrated however by two phenomena too 
minute and delicate for observation without the telescope, but 
accessible to modern methods. One of them is the aberration 
of light, the other the annual parallax of the fixed stars. These 
can be explained only by the actual motion of the earth. We 
reserve their discussion for the present. 

112. The Ecliptic, its Related Points and Circles. — By ob- 
serving daily with the meridian circle the sun's declination, 
and the difference between its right ascension and that of 
some standard star, we obtain a series of positions of the 
sun's centre which can be plotted on a globe, and we can thus 
mark out the path of the sun among the stars. It turns out 
to be a great circle, as is shown by its cutting the celestial 
equator at two points just 180° apart (the so-called " equinoc- 
tial points" or "equinoxes," Art. 34), where it makes an 
angle with the equator of approximately 23|°. 1 This great 
circle is called the Ecliptic, because, as was early discovered, 
eclipses happen only when the moon is crossing it. It may 
be defined as the circle in which the plane of the earth's orbit cuts 
the celestial sphere, just as the celestial equator is the trace of 
the plane of the terrestrial equator. 

The angle which the ecliptic makes with the equator at 
the equinoctial points is called the Obliquity of the Ecliptic. 
This obliquity is evidently equal to the sun's maximum decli- 
nation, or its greatest distance from the equator, reached in 
June and December. 

113. The two points in the ecliptic midway between the 
equinoxes are called the Solstices, because at these points the 

i 23° 27' 08". in 1900. 



§113] 



THE ZODIAC AND ITS SIGNS. 



69 



sun "stands," i.e., ceases to move in declination. Two circles 
drawn through the solstices parallel to the equator are called 
the Tropics, or "turning lines/' because there the sun turns 
from its northward motion to a southward, or vice versa. 

The two points in the heavens 90° distant from the ecliptic 
are called the Poles of the Ecliptic. 

The northern one is in the constellation Draco, about midway 
between the stars Delta and Zeta Draconis, and on the Solstitial Colure 
(the hour-circle which runs through the two solstices), at a distance 
from the pole of the heavens equal to the obliquity of the ecliptic, or 
about 23 J°. Great circles drawn through the poles of the ecliptic, 
and therefore perpendicular, or " secondaries," to the ecliptic, are 
known as Circles of Latitude. It will be remembered (Arts. 38 and 
39) that celestial latitude and longitude are measured with reference to the 
ecliptic and not to the equator. 

114. The Zodiac and its Signs. — A belt 16° wide (8° on each 
side of the ecliptic) is called the Zodiac, or " Zone of Animals •" 
the constellations in it, excepting Libra, being all figures of 
animals. It is taken of that particular width simply because 
the moon and the principal planets always keep within it. 
It is divided into the so-called Signs, each 30° in length, having 
the following names and symbols : — 



Spring 



/ Aries T 
) Taurus 8 
( Gemini n 



( Cancer £5 

Summer < Leo SI 

( Virgo *n 



{ Libra =2= 

Autumn ■) Scorpio ^l 

( Sagittarius / 

rCapricornus VJ 

Winter J Aquarius xz 

( Pisces X 



The symbols are for the most part conventionalized pictures of the 
objects. The symbol for Aquarius is the Egyptian character for water. 
The origin of the signs for Leo, Capricornus, and Virgo is not quite 
clear. 



70 



THE EARTHS ORBIT. 



[§H4 



The zodiac is of extreme antiquity. In the zodiacs of the 
earliest history the Lion, Bull, Ram, and Scorpion appear 
precisely as now. 

115. The Earth's Orbit. — The ecliptic is not the orbit of 
the earth, and must not be confounded with it. It is simply 
a great circle of the infinite celestial sphere, the trace made upon 
that sphere by the plane of the earth's orbit, as was stated 
in its definition. The fact that the ecliptic is a great circle 
gives us no information about the earth's orbit itself, except 
that it all lies in one plane passing through the sun. It tells us 
nothing as to the orbit's real form and size. 

By reducing the observations of the sun's right ascension 
and declination through the year to longitude and latitude 
(the latitude would always be exactly zero except for some 
slight perturbations), and combining these data with observa- 
tions of the sun's ap- 
parent diameter, we can, 
however, ascertain the 
form of the earth's orbit 
and the laic of its motion 
in this orbit. The size 
of the orbit — its scale of 
miles — cannot be fixed 
until we find the sun's 
distance. 

116. To find the Form 
of the Orbit, we proceed 
thus : Take a point : S, 
for the sun, and draw 
from it a line, SO (Fig. 21), directed towards the vernal equi- 
nox, from which longitudes are measured. Lay off from S 
lines indefinite in length, making angles with SO equal to the 
earl's longitude as seen from the sun 1 on each of the days 




Fig. 21. 
Determination of the Form of the Earth's Orbit. 



1 This is 180° -f the sun's longitude as seen from the earth. 



§116] 



DEFINITIONS OF ORBITAL ELLIPSE. 



71 



when observations were made. We shall thus get a sort of 
" spider/' showing the direction of the earth as seen from the 
sun on each of those days. 

Next as to the distances. While the apparent diameter of 
the sun does not tell us its absolute distance from the earth, 
unless we know this diameter in miles, yet the changes in the 
apparent diameter do inform us as to the relative distance at 
different times, the distance being inversely proportional to 
the sun's apparent diameter (Art. 12). If then on this " spider " 
we lay off distances equal to the quotient obtained by dividing 
some constant, say 10000", by the sun's apparent diameter 
at each date, these distances will be proportional to the true 
distance of the earth from the sun, and the curve joining the 
points thus obtained will be a true map of the earth's orbit, 
though without any scale of miles. When the operation is 
performed, we find that the orbit is an ellipse of small " eccen- 
tricity " (about -^), with the sun not in the centre, but at one of 
the two foci. 

117. Definitions relating to the Orbital Ellipse. — The ellipse 
is a curve such that the sum of the two distances from any point 
on its circumference to tivo points within, called the foci, is always 
constant and equal to the so-called major axis of the ellipse. 



In Fig. 22, SP + PF equals 
AA f , A A' being the major axis. 
A C is the semi-major axis, and is 
usually denoted by i or a. BC 
is the semi-minor axis, denoted 
by B or b; the eccentricity, de- ^ 
noted by e, is the fraction or ratio 

— — or -, and is usually expressed 

A C a 

as a decimal. (CS is c). 

If a cone is cut across obliquely 
by a plane, the section is an ellipse, 
which is therefore called one of the 
Art. 506). 



B 



^^^y 


\"~>^ 






^\ \ N. 

w 


\a 


1 F C 


s 

Bi^^ 





Fig. 22. — The Ellipse. 



: Conic Sections " (see Appendix, 



72 LAW OF THE EARTH'S MOTION. [§ 117 

The points where the earth is nearest to and most remote 
from the sun are called respectively the Perihelion and the 
Aphelion, the line joining them being the major-axis of the 
orbit. This line indefinitely produced in both directions is 
called the Line of Apsides, the major-axis being a limited piece 
of it. A line drawn from the sun to the earth or any other 
planet at any point in its orbit, as SP in the figure, is called 
the planet's Radius vector, and the angle ASP, reckoned from 
the perihelion point, A, in the direction of the planet's motion 
towards B, is called its Anomaly. 

The variations in the sun's diameter are too small to be detected 
without a telescope, so that the ancients failed to perceive them. 
Hipparchus, however, about 120 B.C., discovered that the earth is not 
in the centre of the circular 1 orbit which he supposed the sun to de- 
scribe with uniform velocity. Obviously the sun's apparent motion is 
not uniform, because it takes 186 days for the sun to pass from the 
vernal equinox to the autumnal, and only 179 days to return. Hip- 
parchus explained this want of uniformity by the hypothesis that the 
earth is out of the centre of the circle. 

118. To find the Law of the 
Earth's Motion. — By comparing 
the measured apparent diameter 
with the differences of longitude 
from day to day we can deduce 
^ a not only the form of the orbit but 
the "law" of the earth's motion 
in it. On arranging the daily 
motions and apparent diameters 

*ig. 23. — Equable Description of Areas. t rr 

in a table, we find that the daily 
motions vary directly as the squares of the diameters. From this 

1 He (and every one else until the time of Kepler) assumed on meta- 
physical grounds that the sun's orbit must necessarily be a circle, and 
described with a uniform motion, because (they said) the circle is the 
only perfect curve, and uniform motion is the only perfect motion proper 
to heavenly bodies. 




§118] 



KEPLEK S PROBLEM. 



73 



it can be shown to follow that the earth moves in such a way 
that its radius ^ector describes areas proportional to the times, a 
law which Kepler first brought to light in 1609. That is to 
say, if ab, cd, and ef, Fig. 23, be portions of the orbit described 
by the earth in different weeks, the areas of the elliptical 
sectors aSb, cSd, and eSf are all equal. A planet near peri- 
helion moves faster than at aphelion in just such proportion 
as to preserve this relation. 

119. Kepler's Problem. — As Kepler left the matter, this is 
a mere fact of observation. Newton afterwards demonstrated 
that it is a necessary mechanical consequence of the fact that 
the earth moves under the action of a force ahvays directed 
towards the sun (see Appendix, Art. 502). It is true in every 
case of elliptical motion, and enables us to find the position of 
the earth, or any planet, at any 
time when we once know the 
time of its orbital revolution 
(technically the i( period ") and 
the time when it was at peri- 
helion. Thus, the angle ASP, 
Fig. 24, or the anomaly of the 
planet, must be such that the 
shaded area of the elliptical sec- 
tor ASP will be that portion 

of the whole ellipse which is represented by the fraction — , t 

being the number of days since the planet last passed peri- 
helion, and T the number of days in the whole period. 

If, for instance, the earth last passed perihelion on Dec. 31st (which 
it did), its place on May 1st must be such that the sector ASP will be 

121 

r-— : of the whole of the earth's orbit, since it is 121 days from Dec. 
365^ J 

31st to May 1st. The solution of this problem, known as Kepler's 

Problem, leads to " transcendental " equations, and can be found in 

books on Physical Astronomy. 




Fig. 24. — Kepler's Problem. 



74 CHANGES IN THE EARTH'S ORBIT. [§ 120 

120. Changes in the Earth's Orbit. — The orbit of the earth 
changes slowly inform and position, though it is unchangeable 
(in the long run) as regards the length of its major axis and 
the duration of the year. 

(1) Change in the Obliquity of the Ecliptic. The ecliptic slightly 
and very slowly shifts its position among the stars, thus altering their 
latitudes and the angle between the ecliptic and the equator. The 
obliquity is at present about 24' less than it was 2000 years ago, and 
is still decreasing about 0".5 a year. It is computed that this diminu- 
tion will continue for some 15,000 years, reducing the obliquity to 
about 22 J°, when it will begin to increase. The whole change can 
never exceed 1J° on each side of the mean. 

(2) Change of Eccentricity. At present the eccentricity of the earth's 
orbit (which is now 0.0168) is also slowly diminishing. According 
to Leverrier, it will continue to decrease for about 24,000 years until 
it becomes 0.003 and the orbit is almost circular. Then it will 
increase again for some 40,000 years until it becomes 0.02. In this 
way the eccentricity will oscillate backwards and forwards, always, 
however, remaining between zero and 0.07; but the successive oscilla- 
tions of both the eccentricity and obliquity are unequal in amount 
and in time, so that they cannot properly be compared to the " vibra- 
tions of a mighty pendulum," which is rather a favorite figure of 
speech in certain quarters. 

(3) Revolution of the Apsides of the Earth's Orbit. The line of 
apsides of the orbit (which now stretches in both directions towards 
the opposite constellations of Sagittarius and Gemini) is also slowly 
and steadily moving eastward at a rate which will carry it around the 
circle in about 108,000 years. 

These so-called "secular" changes are due to "perturbations" caused 
by the action of the other planets upon the earth. Were it not for 
their attraction, the earth would keep her orbit with reference to the 
sun strictly unaltered from age to age, except that possibly in the 
course of millions of years the effects of falling meteoric matter and 
of the attraction of the nearer fixed stars might become perceptible. 

121. Besides these secular perturbations of the earth's Orbit, the 
earth itself is continually being slightly disturbed in its orbit. On 
account of its connection with the moon, it oscillates each month a 



§ 121] PRECESSION OF THE EQUINOXES. 75 

few hundred miles above and below the true plane of the ecliptic, and 
by the action of the other planets it is sometimes set forward or back- 
ward in its orbit to the extent of some thousands of miles. Of course 
every such displacement produces a corresponding slight change in 
the apparent position of the sun. 

122. Precession of the Equinoxes. — The length of the year 
was found in two ways by the ancients : — 

1st. By observing the time when the shadow cast at noon 
by a " gnomon " is longest or shortest : this determines the 
date of the solstice, 

2d. By observing the position of the sun with reference to 
the constellations — their "heliacal" rising and setting, — i.e., 
the times when given constellations rise and set at sunset. 

Comparing the results of observations made by these two 
methods at long intervals, Hipparchus in the second century 
b.c. found that they do not agree, the year reckoned from solstice 
to solstice or from equinox to equinox being about twenty min- 
utes shorter than the year reckoned tvith inference to the constel- 
lations. The equinox moves westward on the ecliptic about 
50".2 each year, as if advancing to meet the sun at each annual 
return. He therefore called this motion of the equinoxes 
" Precession" 

On examining the latitudes of the stars, we find them to have 
changed but slightly in the last 2000 years. We know therefore that 
the ecliptic maintains its position sensibly unaltered. The right ascen- 
sions and declinations of the stars, on the other hand, are found to be 
both constantly changing, and this makes it certain that the celestial 
equator shifts its position. On account of the change in the place of 
the equinox, the longitudes of the stars grow uniformly larger, having 
increased nearly 30° in the last 2000 years. 

123. Motion of the Pole of the Heavens around the Pole of 
the Ecliptic — The obliquity of the ecliptic, which equals the 
angular distance of the pole of the heavens from the pole of 
the ecliptic, is not sensibly affected by precession. That is to 



76 



PRECESSION OF THE EQUINOXES. 



[§ 123 



say, — as the earth travels around its orbit in the plane 
of the ecliptic (just as if that plane were the level sur- 
face of a sheet of water in which the earth swims half im- 
mersed), its axis, AOX (Fig. 25), always preserves the same 
constant angle of 23^-° with the perpendicular SOT which 

points to the pole of 
the ecliptic. But in 
consequence of pre- 
cession, the axis while 
keeping its inclina- 
tion unchanged, shifts 
conically around the 
line SOT (like the 
axis of a spinning 
top before it becomes 
steady), taking up 
successively the posi- 
tions A'O, etc., thus 
carrying the equinox 
from V to V, and so 
on. 

In consequence of 
this shift of the axis, 
the pole of the heavens, i.e., that point in the sky to which 
the line CA happens to be directed at any time, describes a 
circle around the pole of the ecliptic in a period of about 
25,800 years (360° -r- 50.2"). The pole of the ecliptic remains 
practically fixed among the stars, but the pole of the equator 
has moved many degrees since the earliest observations. At 
present the Pole-star (Alpha Ursae Minoris) is about 1£° from 
the pole, while in the time of Hipparchus the distance was 
fully 12° ; during the next century it will diminish to about 
30', and then it will increase again. 

If upon a celestial globe we take the pole of the ecliptic as a centre 
and describe around it a circle with a radius of 23J°, it will mark the 




Fig. 25. 



§ 123] PHYSICAL CAUSE OF PRECESSION. 77 

track of the celestial pole among the stars. It passes pretty near 
the star Vega ( Alpha Lyrae) , on the opposite side of the circle from 
the present Pole-star ; so that, abont 12,000 years hence, Vega will 
be the Pole-star, — a splendid one. 

Reckoning backwards, we find that abont 4000 years ago Alpha 
Draconis was the Pole-star, and abont 3J° from the pole. 

Another effect of precession is that the signs of the zodiac 
do not now agree with the constellations which bear the same 
name. The sign of Aries is now in the constellation of Pisces, 
and so on; each sign having "backed" bodily, so to speak, 
into the constellation west of it. 

N. B. This precessional motion of the celestial pole mnst not be 
confounded with the motion of the terrestrial pole which causes vari- 
ation of latitude (Art. 71*). 

124. Physical Cause of Precession. — The physical cause of 
this slow conical rotation of the earth's axis around the pole 
of the ecliptic was first explained by Newton, and lies in the 
two facts that the earth is not exactly spherical, and that the 
sun and moon 1 act upon the equatorial "ring" of matter 
which projects above the true sphere, tending to draw the 
plane of the equator into coincidence with the plane of the 
ecliptic by their greater attraction on the nearer portions of 
the "ring." 

If it were not for the earth's rotation, this action of the sun and 
moon would bring the two planes of the ecliptic and the equator into 
coincidence ; but since the earth is spinning on its axis, we get the 
same result that we do with the whirling wheel of a gyroscope, by 
hanging a weight at one end of the axis. We then have a combina- 
tion of two rotations at right angles to each other, one the whirl 



1 The planets exert a very slight influence upon the motion of the equi- 
nox, not, however, by producing a true precession, but by slightly disturb- 
ing the position of the plane of the earth's orbit (Art. 120 (1)). This 
effect is in the opposite direction from the true precession produced by 
the sun and moon, and is about 0'M6 annually. 



78 



PHYSICAL CAUSE OF PRECESSION. 



[§124 



of the wheel, the other the "tip" which the weight tends to give 
the axis. Compared with the mass of the earth and its energy of 
rotation this disturbing force is very slight, and consequently the 
rate of precession extremely slow. Our space does not permit a dis- 
cussion of the manner in which the forces operate to produce the 
peculiar result. For this, as also for an account of the so-called 
Equation of the Equinoxes and Nutation, the reader is referred to higher 
text-books. 



125. Aberration. — The fact that light is not transmitted 
instantaneously, but with a finite velocity, causes the apparent 
displacement of an object viewed from any moving station, 
unless the motion is directly towards or from that object. If 
the motion of the observer is slow, this displacement or "aber- 
ration " is insensible ; but the earth moves so swiftly (18^ 
miles per second) that it is easily observable in the case of the 
stars. Astronomical aberration may be defined, therefore, as 
the apparent displacement of a heavenly body due to the combina- 
tion of the orbital motion of the earth with that of light. The 
direction in which we have to point our telescope in observing 
a star is not the same as if we were at rest. 

We may illustrate this by 
considering what would hap- 
pen in the case of falling rain- 
drops observed by a person in 
motion. Suppose the observer 
standing with a tube in his 
hand while the drops are fall- 
ing vertically : if he wishes to 
have the drops descend axially 
through the tube without touch- 
ing the sides, he must obviously 
keep it vertical so long as he 
stands still ; but if he advances 
in any direction the drops will strike his face and he must draw back 
the bottom of the tube (Fig. 26) by an amount which equals the 
advance he makes while a drop is falling through it ; i.e., he must 




Fig. 26. — Aberration of a Raindrop. 



§ I 25 ] EFFECT OF ABERRATION. 79 

incline the tube forward at an angle, 1 a, depending both upon the ve- 
locity of the rain-drop and the velocity of his own motion, so that 
when the drop, which entered the tube at B, reaches A r , the bottom 
of the tube will be there also. 

It is true that this illustration is not a demonstration, because light 
does not consist of particles coming towards us, but of waves trans- 
mitted through the ether of space. But it has been shown (though 
the proof is by no means elementary) that within very narrow limits, 
the apparent direction of a wave is affected in precisely the same way 
as that of a moving projectile. 

126. The Effect of Aberration on the Place of a Star. — The 

velocity of light being 186,330 miles per second (according to 
the latest experiments of Newcomb and Michelson) while that 
of the earth in its orbit is 18.5 miles, we find that a star, 
situated on a line at right angles to the direction of the earth's 
motion, is apparently displaced by an angle which equals 

(The Astronomical Congress of 1896 adopted the value, 20".47.) 

This is the so-called " Constant of Aberration." 

If the star is in a different part of the sky its displacement 

will be less, the amount being easily calculated when the star's 

position is given. 

A star at the pole of the ecliptic being permanently in a direction 
perpendicular to the earth's motion, will always be displaced by the 
same amount of 20". 5, but in a direction continually changing. It must 
therefore appear to describe during the year a little circle, 41" in 
diameter. 

A star on the ecliptic appears simply to oscillate back and forth in 
a straight line 41" long. In general, the " aberrational orbit " is an 
ellipse, having its major axis parallel to the ecliptic and always 41" 
long, while its minor axis depends upon the star's latitude. 

1 Tang a— ^, or (when a is small) a = 206265"^, where u is the veloc- 
ity of the observer and Fthat of the drop. 



80 THE SUN'S DISTANCE BY ABERRATION. f§ 127 

127. Determination of the Sun's Distance by means of the 
Aberration of Light. — Since (foot-note to Art. 125) 

a"= 206265 - , u = — ^— V. 
V 206265 

When, therefore, we have ascertained the value of a" (20 ".47) 
from observations of the stars, and of V (186,330 miles) by 
physical experiments, we can immediately find u, the velocity 
of the earth in her orbit. The circumference of the earth's 
orbit is then found by multiplying this velocity, w, by the 
number of seconds in a sidereal year (Art. 133), and from this 
we get the radius of the orbit, or the earth's mean distance from 
the sun, by dividing the circumference by 27r. Using the 
values above given, the mean distance of the sun comes out 
92,877,000 miles. But the uncertainty of a" is probably as 
much as 0".03, and this affects the distance proportionally, 
say one part in 600, or 150,000 miles. Still the method is one 
of the very best of all that we possess for determining in 
miles the value of " the Astronomical Unit." See Appendix, 
Chap. XV. 

CONSEQUENCES OF THE EARTH'S ORBITAL MOTION. 

128. Solar Time and the Equation of Time. — Since the sun 
makes the circuit of the heavens in a year, moving always 
towards the east, the solar day, or the interval between the 
two successive transits of the sun across any observer's merid- 
ian, is longer than that between two transits of a given star, or 
twenty-four sidereal hours. The difference must amount to 
exactly one day in a year ; i.e., while in a year there are 366^ 
(nearly) sidereal days, there are only 365£ solar days. The 
average daily difference is therefore a little less than 4 m . 

Moreover, the sun's advance in right ascension between two 
successive noons varies materially, so that the apparent solar 
days are not all of the same length. Accordingly, as explained 



§ 128] CONSEQUENCES OF EARTH'S ORBITAL MOTION. 81 

in Arts. 54 and 55, mean time has been adopted, which is kept 
by & fictitious or mean sun, moving uniformly in the equator 
at the same average rate as that of the real sun in the ecliptic. 
The hour-angle of this mean sun is the local mean time, or 
clock time, while the hour-angle of the real sun is the apparent 
or sun-dial time. 

The " equation of time " is the difference between these two 
times, reckoned as plus when the sun-dial is slower than the 
clock and minus when it is faster, i.e., it is the "correction " which 
must be added (algebraically) to apparent time in order to get 
mean time. 1 

The principal causes of this difference are two. 

1. The variable motion of the sun in the ecliptic due to the 
eccentricity of the earth's orbit. 

2. The obliquity of the ecliptic. 

For an explanation of the manner in which these causes operate, 
see Appendix, Arts. 497-499. 

The two causes mentioned are, however, only the principal ones. 
Every perturbation suffered by the earth comes in to modify the 
result ; but all the other causes combined never affect the equation of 
time by more than a very few seconds. 

The equation of time becomes zero four times a year, viz., 
about April 15th, June 14th, Sept. 1st, and Dec. 24th. The max- 
ima are Feb. 11th, + 14 m 32 s ; May 14th, - 3 m 55 s ; July 26th, 
+6 ra 12 s ; and Nov. 2d, - 16 m 18 s ; but the dates and amounts 
Tr ary slightly from year to year. 

129. The Seasons. — The earth in its annual motion keeps 
its axis always nearly parallel to itself, for the mechanical 
reason that a spinning body maintains the direction of its axis 

1 Since it is the difference between the hour-angles of the fictitious and 
real suns at any moment, it may also be defined as the difference between 
their right ascensions; or, as a formula, we may write E = a t — a mi in which 
a m is the right ascension of the mean sun, and a t that of the true sun. 



82 DIURNAL PHENOMENA NEAR THE POLE. [§ 129 

invariable, unless disturbed by extraneous force (very prettily 
illustrated by the gyroscope). On March x 20th, the earth is 
so situated that the plane of its equator passes through the 
sun. At that time, therefore, the circle which bounds the 
illuminated portion of the earth passes through the two poles, 
and day and night are everywhere equal, as implied by the term 
" equinox." The same is again true on the 22d of September. 
About the 21st of June, the earth is so situated that its north 
pole is inclined towards the sun by about 23^°. The south 
pole is then in the obscure half of the earth's globe, while the 
north pole receives sunlight all day long ; and in all portions 
of the northern hemisphere the day is longer than the night, 
the difference depending upon the latitude of the place : in the 
southern hemisphere, on the other hand, the days are shorter 
than the nights. At the time of the winter solstice these con- 
ditions are, of course, reversed, and the southern pole has the 
perpetual sunshine. 

At the equator of the earth the day and night are equal at 
all times of the year, and in that part of the earth there are 
no seasons in the proper sense of the word. 

130. Diurnal Phenomena near the Pole. The Midnight Sun. 

— At the north pole of the earth, where the celestial pole is in the 
zenith and the diurnal circles are parallel with the horizon (Art. 42), 
the sun will maintain the same elevation all day long, except for the 
slight change caused by its motion in declination during 24 hours. 
The sun will appear on the horizon at the date of the vernal equinox 
(in fact, about two days before it, on account of refraction), and 
will slowly wind upwards in the sky until it reaches its maximum 
elevation of 23J degrees on June 21st. Then it will retrace its course 
until two or three days after the autumnal equinox, when it sinks out 
of sight. 

At points between the north pole and the polar circle the sun will 
appear above the horizon earlier in the year than March 20th, and 
will rise and set daily until its declination becomes equal to the observ- 
er's distance from the pole. It will then make a complete circuit of the 
heavens daily, never setting again until it reaches the same decli- 



§130] 



EFFECTS ON TEMPERATURE. 



83 



nation in its southward course, after passing the solstice. From that 
time it will again rise and set daily until it reaches a southern declina- 
tion just equal to the observer's polar distance. Then the long night 
begins, and continues until the sun, having passed the southern sol- 
stice, returns again to the same declination at which it made its 
appearance in the preceding spring. 

At the polar circle itself, or, more strictly speaking, owing to refrac- 
tion, about |° south of it, the "midnight sun" will be seen on just one 
day in the year — the day of the summer solstice. 

131. Effects on Temperature. — The changes in the duration 
of "insolation" (exposure to sunshine) at any place involve 
changes of temperature and of other climatic conditions, thus 
producing the Seasons. Taking as a standard the amount of 
heat received in twenty-four hours on the day of the equinox, 
it is clear that the surface of the soil at any place in the 
northern hemisphere will receive daily from the sun more than 
this average amount of heat whenever he is north of the celes- 
tial equator ; and for two reasons : — 

1. Sunshine lasts more than half the day. 

2. The mean altitude of the sun during the day is greater 
than at the time of the equinox, since he is higher at noon 
and in any case reaches the hori- 
zon at rising and setting. Now 
the more obliquely the rays 
strike, the less heat they bring 
to each square inch of the sur- 
face, as is obvious from Fig. 27. 
A beam of sunshine having a 
cross section, ABCD, when it 
strikes the surface at an angle, 
h, (equal to the sun's altitude) 
is spread over a much larger 

surface, Ac, than when it strikes perpendicularly. This differ- 
ence in favor of the more nearly vertical rays is exaggerated 
by the absorption of heat in the atmosphere, because rays that 




Fig. 27. 

Effect of Sun's Elevation on Amount of 

Heat imparted to the Soil. 



84 TIME OP HIGHEST TEMPERATURE. [§ 131 

are nearly horizontal have to traverse a much greater thick- 
ness of air before reaching the ground. 

For these two reasons, therefore, the temperature rises rap- 
idly at a place in the northern hemisphere as the sun comes 
north of the equator. 

132. Time of Highest Temperature. — We, of course, receive 
the most heat in twenty-four hours at the time of the summer 
solstice ; but this is not the hottest time of summer for the 
obvious reason that the weather is then getting hotter, and the 
maximum will not be reached until the increase ceases ; i.e., 
not until the amount of heat lost in twenty-four hours equals that 
received. The maximum is reached in our latitude about the 
1st of August. For similar reasons the minimum temperature 
of winter occurs about Feb. 1st. 

Since, however, the weather is not entirely "made on the spot 
where it is used," but is much influenced by winds and currents that 
come from great distances, the actual time of the maximum tempera- 
ture at any particular place cannot be determined by mere astronom- 
ical considerations, but varies considerably from year to year. 

133. The Three Kinds of Year. — Three different kinds of 
"year" are now recognized, — the Sidereal, the Tropical (or 
Equinoctial), and the Anomalistic, 

The sidereal year, as its name implies, is the time occupied 
by the sun in apparently completing the circuit from a given 
star to the same star again. Its length is 365 days, 6 hours, 
9 minutes, 9 seconds. 

From the mechanical point of view, this is the true year; i.e., it is the 
time occupied by the earth in completing its revolution around the 
sun from a given direction in space to the same direction again. 

The tropical year is the time included between two succes- 
sive passages of the vernal equinox by the sun. Since the 
equinox moves yearly, 50".2 towards the west (Art. 122), this 



§ 133] THE CALENDAR. 85 

tropical year is shorter than the sidereal by about 20 minutes, 
its length being 365 days, 5 hours, 48 minutes, 46 seconds. 

Since the seasons depend on the sun's place with respect to the 
equinox, the tropical year is the year of chronology and civil 
reckoning. 

The third kind of year is the anomalistic year, the time be- 
tween two successive passages of the perihelion by the earth. 
Since the line of apsides of the earth's orbit makes an east- 
ward revolution once in about 108,000 years (Art. 120), this 
'kind of year is nearly 5 minutes longer than the sidereal, its 
length being 365 days, 6 hours, 13 minutes, 48 seconds. 

It is but little used, except in calculations relating to perturbations. 

134. The Calendar. — The natural units of time are the day, 
the month, and the year. The day is too short for conveni- 
ence in dealing with considerable periods, such as the life of a 
man, for instance, and the same is true even of the month, so 
that for all chronological purposes the tropical year (the year 
of the seasons) has always been employed. At the same 
time, so many religious ideas and observations have been con- 
nected with the change of the moon, that there has been a 
constant struggle to reconcile the month with the year. Since, 
however, the two are incommensurable, no really satisfactory 
solution is possible, and the modern calendar of civilized 
nations entirely disregards the lunar phases. 

In the earliest times the calendar was in the hands of the priest- 
hood and was predominantly lunar, the seasons being either disre- 
garded or kept roughly in place by the occasional intercalation or the 
dropping of a month. - The Mohammedans still use a purely lunar 
calendar, having a "year" of 12 months, containing alternately 354 
and 355 days. In their reckoning the seasons fall continually in dif- 
ferent months, and their calendar gains on ours about one year in 
thirty-three. 



86 THE METONIC CYCLE AND GOLDEN NUMBER. [§ 135 

135. The Metonic Cycle and Golden Number. — Meton, a 
Greek astronomer, about 433 B.C., discovered that a period of 235 
months is very nearly equal to 19 years of 365 J days each, the differ- 
ence being hardly more than two hours. It follows that every 19th 
year the new moons recur on the same days of the month ; so that, 
as far as the moon's phases are concerned, the almanacs of 1880 and 
1899, for instance, would agree (but the way in w T hich the intervening 
leap years come in may make a difference of one day). 

The golden number of the year is its number in this Metonic cycle. 
It is found by adding 1 to the "date number " of the year and divid- 
ing by 19 : the remainder is the golden number, unless it comes out 
zero, in which case 19 itself is taken. Thus the golden number of 
1890 is found by dividing 1891 by 19; the remainder, 10, is the golden 
number of the year. This number is still employed in the ecclesiasti- 
cal calendar for finding the date of Easter. 

136. The Julian Calendar. — When Julius Caesar came into 
power he found the Roman Calendar in a state of hopeless con- 
fusion. He, therefore, sought the advice of the astronomer 
Sosigenes, and in accordance with his suggestions established 
(b.c. 45) what is known as the Julian Calendar, which still, 
either untouched or with a trifling modification, continues in 
use among all civilized nations. Sosigenes discarded all con- 
sideration of the moon's phases, and adopting 365^ days as 
the true length of the year, he ordained that every fourth 
year should contain 366 days, the extra day being inserted by 
repeating the sixth day before the Calends of March, whence 
such a year is called "Bissextile." He also transferred the 
beginning of the year, which before Caesar's time had been in 
March (as indicated by the names of several of the months, - — 
December, the tenth month, for instance) to January 1st. 

Caesar also took possession of the month Quintilis, naming it July 
after himself. His successor, Augustus, in a similar manner appro- 
priated the next month, Sextilis, calling it August, and to vindicate 
his dignity and make his month as long as his predecessor's, he added 
to it a day filched from February. 



§ 136] THE GREGORIAN CALENDAR. 87 

The Julian Calendar is still used unmodified in the Greek 
Church, and also in many astronomical reckonings. 

137. The Gregorian Calendar. — The true length of the 
tropical year is not 365^ days, but 365 days, 5 hours, 48 
minutes, 46 seconds, leaving a difference of 11 minutes and 14 
seconds by which the Julian year is too long. This difference 
amounts to a little more than three days in 400 years. As a 
consequence, the date of the vernal equinox comes continually 
earlier and earlier in the Julian calendar, and in 1582 it had 
fallen back to the 11th of March instead of occurring on the 
21st, as it did at the time of the Council of Nice, a.d. 325. 
Pope Gregory, therefore, under the astronomical advice of 
Clavius, ordered that the calendar should be restored by 
adding ten days, so that the day following Oct. 4th, 1582, 
should be called the 15th instead of the 5th ; further, to pre- 
vent any future displacement of the equinox, he decreed that 
thereafter only such " century years " should be leap years as 
are divisible by 400. (Thus 1700, 1800, 1900, 2100, and so 
forth, are not leap years, but 1600 and 2000 are.) 

138. The change was immediately adopted by all Catholic countries, 
but the Greek Church and most Protestant nations refused to recognize 
the Pope's authority. The new calendar was, however, at last adopted 
in England by an act of Parliament passed in 1751. It provided that 
the year 1752 should begin on Jan. 1st (instead of March 25th, as 
had long been the rule in England), and that the day following Sept. 
2d, 1752, should be reckoned as the 14th instead of the 3d, thus drop- 
ping 11 days. At present (since the year 1800 was a leap year in the 
Julian calendar and not in the Gregorian) the difference between the 
two calendars is 12 days. Thus, in Russia the 22d of June is reck- 
oned the 10th ; but in that country both dates are ordinarily used for 
scientific purposes, so that the date mentioned would be written 
June ||. When Alaska was annexed to the United States, the official 
dates had to be changed by only eleven days, one day being provided 
for by the alteration from the Asiatic date to the American (Art. 
G6). 



88 THE MOON. [§ 139 



CHAPTER V. 

THE MOON. — HER ORBITAL MOTION AND THE MONTH. — 
DISTANCE, DIMENSIONS, MASS, DENSITY, AND FORCE OF 
GRAVITY. — ROTATION AND LIBRATIONS. — PHASES. — 
LIGHT AND HEAT. — PHYSICAL CONDITION. — TELE- 
SCOPIC ASPECT AND PECULIARITIES OF THE LUNAR 
SURFACE. 

139. Next to the sun, the moon is the most conspicuous 
and to us the most important of the heavenly bodies : in fact, 
she is the only one except the sun, which exerts the slightest 
influence upon the interests of human life. If the stars and 
the planets were all extinguished, our eyes would miss them, 
and that is all. But if the moon were annihilated, the inter- 
ests of commerce would be seriously affected by the practical 
cessation of the tides. She owes her conspicuousness and 
her importance, however, solely to her nearness, for she is 
really a very insignificant body as compared with stars and 
planets. 

140. The Moon's Apparent Motion, Definition of Terms, etc. 

— One of the earliest observed of astronomical phenomena 
must have been the eastward motion of the moon with refer- 
ence to the sun and stars, and the accompanying change of 
phase. If, for instance, we note the moon to-night as very 
near some conspicuous star, we shall find her to-morrow night 
at a point considerably farther east, and the next night farther 
yet ; she changes her place about 13° daily and makes a com- 
plete circuit of the heavens, from star to star again, in about 
27-J- days. In other words, she revolves around the earth in 



§ 1^0] SIDEREAL AND SYNODIC MONTHS. 89 

that time, while she accompanies us in our annual journey 
around the sun. 

Since the moon moves eastward among the stars so much 
faster than the sun (which takes a year in going once around), 
she overtakes and passes him at regular intervals ; and as her 
phases depend upon her apparent position with reference to 
the sun, this interval from new moon to new moon is specially 
noticeable and is what we ordinarily understand as the 
"month." 

The angular distance of the moon east or west of the sun at 
any time is called her "Elongation" l At new moon it is zero, 
and the moon is said to be in " Conjunction" At full moon 
the elongation is 180°, and she is said to be in " Opposition." 
In either case the moon is in u Syzygy"; i.e., the sun, moon, 
and earth are arranged along a straight line. When the elon- 
gation is 90° she is said to be in " Quadrature." 

141. Sidereal and Synodic Months. — The sidereal month is 
the time it takes the moon to make her revolution from a given 
star to the same star again. It averages 27 days, 7 hours, 43 
minutes, 11.55 seconds, or 27.32166 days, but varies some 3 
hours on account of " perturbations." The mean daily motion 
is 360° ~ 27.32166, or 13° 11'. Mechanically considered, the 
sidereal month is the true one. 

The synodic month is the time between two successive conjunc- 
tions or oppositions ; i.e., between successive new or full moons. 
Its average value is 29 days, 12 hours, 44 minutes, 2.864 sec- 
onds, but it varies 13 h , mainly on account of the eccentricity 
of the lunar orbit. As has been said already, this synodic 
month is what we ordinarily understand by the term "month." 

1 There is a slight difference between elongation in right ascension and 
elongation in longitude, and a corresponding difference between con- 
junction and opposition in right ascension and longitude respectively. 
Conjunction in right ascension occurs when the difference of right ascension 
of the sun and moon is zero; conjunction in longitude when the difference 
of longitude (reckoned on the ecliptic, it will be remembered) is zero. 



90 THE MOON'S PATH. [§ HI 

If M be the length of the moon's sidereal period, E the length of the 
sidereal year, and S that of the synodic month, the three quantities 
are connected by a simple relation which is easily demonstrated. 

— is the fraction of a circumference moved over by the moon in a 

M . i . 

day. Similarly _ is the apparent daily motion of the sun. The dif- 

E 
ference is the amount which the moon gains on the sun daily. Now 
it gains a whole revolution in one synodic month of S days, and there- 
fore must gain daily — of a circumference. Hence we have the im- 
portant equation 

M E~ S 

Another way of looking at the matter, leading, of course, to the 
same result is this : — In a sidereal year the number of sidereal 
months must be just one greater than the number of synodic months : 
the numbers are respectively 13.369+ and 12.369 + . 

142. The Moon's Path among the Stars. — By observing the 
moon's right ascension and declination daily with the meridian 
circle or other suitable instruments, we can map out its appar- 
ent path, just as in the case of the sun (Art. 112). This path 
turns out to be (very nearly) a great circle, inclined to the 
ecliptic at an angle of about 5° 8 f . The two points where it 
cuts the ecliptic are called the Nodes, the ascending node being 
the one where the moon passes from the south side to the 
north side of the ecliptic, while the opposite node is called 
the descending node. 

The moon at the end of the month never comes back exactly 
to the point of beginning among the stars, on account of the so- 
called "perturbations/' due mostly to the attraction of the sun. 
One of the most important of these perturbations is the ''re- 
gression of the nodes." These slide westward on the ecliptic 
just as the vernal equinox does (precession), but much faster, 
completing their circuit in about 19 years instead of 26,000. 

When the ascending node of the moon's orbit coincides with the 
vernal equinox, the angle between the moon's path and the celestial 



§ 1^2] INTERVAL BETWEEN MOON'S TRANSITS. 91 

equator is 23° 28' + 5° 8', or 28° 36'; 9.} years later, when the descend- 
ing node has come to the same point, the angle is only 23° 28' — 5° 8', 
or 18° 2(y. In the first case the moon's declination will range during 
the month from +28° 36' to —28° 36', which makes a difference of 
more than 57° in its meridian altitude. In the second case the whole 
range is reduced to 36° 40'. 

143. Interval between the Moon's Successive Transits ; Daily 
Retardation of its Rising and Setting. — Owing to the east- 
ward motion of the moon, it comes to the meridian later each 
day by about 51 m on the average ; but the retardation ranges 
all the way from 38 minutes to 66 minutes, on account of the 
variations in the rate of the moon's motion in right ascension. 
These variations are due to the oval form of its orbit and to 
its inclination to the celestial equator, and are precisely analo- 
gous to those of the sun's motion, which produce " the equa- 
tion of time " (Art. 128) ; but they are many times greater. 

The average retardation of the moon's daily rising and set- 
ting is also, of course, the same 51 m , but the actual retardation 
is still more variable than that of the transits, depending, as 
it does, to some extent on the latitude of the observer as well 
as on the variations in the moon's motion. At New York 
the range is from 23 minutes to 1 hour and 17 minutes. In 
higher latitudes it is still greater. 

In latitudes above 61° 30' the moon, when it has its greatest possi- 
ble declination of 28° 36' (Art. 142), will become circumsolar for a 
certain time each month, and will remain visible without setting at 
all (like the "midnight sun") for a greater or less number of day?, 
according to the latitude of the observer. 

144. Harvest and Hunter's Moon. — The full moon that 
occurs nearest the autumnal equinox is known as the harvest 
moon, the one next following as the hunter's moon. At that 
time of the year the moon while nearly full rises for several 
consecutive nights nearly at the same hour, so that the moon- 
light evenings last for an unusually long time. The phenome- 



92 FORM OF THE MOON'S ORBIT. [§ 1*4 

non, however, is much more striking in Northern Europe than 
in the United States. 

At this time of the year the full moon is near the vernal equinox, 
and in that portion of its path which is the least inclined to the 
eastern horizon. This is obvious from Fig. 28, which represents 
a celestial globe looked at from the east. HN is the horizon, E the 
east point, P the pole, and EQ the equator. If, now, the first of 
Aries is rising at E, the line JEJ' will be the ecliptic and will be 




Fig. 28. — Explanation of the Harvest Moon. 

inclined to the horizon at an angle less than QEH by 23. J°, which is 
the inclination of the equator. If, on the other hand, the first of Libra 
is rising, the ecliptic will be the line DED' '. If the ascending node of 
the moon's orbit happens to coincide with the first of Aries, then, 
when this node is rising, the moon's path will lie still more nearly 
horizontal than JJ', as shown by the dotted line MEM', 

145. Form of the Moon's Orbit. — By observation of the 
moon's apparent diameter in connection with observations of 
her place in the sky, we can determine the form of her orbit 
around the earth in the same way that the form of the earth's 
orbit around the sun was worked out in Art. 116. The moon's 
apparent diameter ranges from 33' 33" when as near as pos- 
sible, to 29' 24" when most remote. (Ncison.) 

The orbit turns out to be an ellipse like that of the earth 
around the sun, but one of much greater eccentricity, avera- 



§ 145] PARALLAX. 93 

ging about y 1 -^ (as against -fa). We say " averaging" because 
it varies from t l to £ T on account of perturbations. 

The point of the moon's orbit nearest the earth is called the 
perigee, that most remote, the apogee, and the indefinite line 
passing through these points, the line of apsides, while the 
major axis is that portion of this line which lies between the 
perigee and apogee. This line of apsides is in continual motion 
on account of perturbations (just as the line of nodes is — Art. 
142) ; but it moves eastward instead of westward, completing 
its revolution in about nine years. 

In her motion around the earth the moon also observes the 
same law of equal areas that the earth does in her orbit around 
the sun. 

THE MOON'S DISTANCE. 

146. In the case of any heavenly body one of the first and 
most fundamental inquiries relates to its distance from us : 
until the distance has been somehow measured we can get no 
knowledge of the real dimensions of its orbit, nor of the size, 
mass, etc., of the body itself. The problem is usually solved 
by measuring the apparent " parallactic " displacement of the 
body due to a known change in the position of the observer. 
Before proceeding farther we must therefore briefly discuss 
the subject of parallax. 

147. Parallax. — -In general the word "parallax" means the 
difference between the directions of a heavenly body as seen 
by the observer and as seen from, some standard point of 
reference. The "annual" or "heliocentric" parallax of a star 
is the difference of the star's direction as seen from the earth 
and from the sun. The "diurnal" or "geocentric" parallax of 
the sun, moon, or a planet, is the difference of its direction 
as seen from the centre of the earth and from the observer's 
station on the earth's surface, or what comes to the same 
thing, it is the angle at the body made by the two lines drawn 



94 



PARALLAX AND DISTANCE. 



[§147 



from it, one to the observer, the other to the centre of the earth. 

In Fig. 29 the parallax of the body, P, is the angle OPC, 

which equals xOP, and is the 
difference between ZOP and 
ZCP. Obviously this parallax 
is zero for a body directly over- 
head at Z, and a maximum 
for a body just rising at P h 
Moreover, and this is to be 
specially noted, this parallax 
of a body at the horizon — 
" the horizontal parallax " — is 
simply the angular semi-diame- 
ter of the earth as seen from the 
body. When we say that the 

moon's horizontal parallax is 57', it is equivalent to saying that 

seen from the moon the earth appears to have a diameter of 114'. 

148. Relation between Parallax and Distance. — When the 
horizontal parallax of any heavenly body is ascertained, its 
distance follows at once through our knowledge of the earth's 
dimensions. From Art. 12 we have the equation 




Fig. 29. — Diurnal Parallax. 



r=E 



s" \ 
206265 J' 



in which r is the earth's radius, E the distance of the body, 
and s n the apparent semi-diameter of the earth (in seconds of 
arc) as seen from the body ; i.e., s n = the body's " horizontal 
parallax." If, as is usual, we write p" instead of s" for the 
horizontal parallax of the body, this gives 

iJ= /206265\ 



"V~P ,r 7 



This implies, of course, that a body whose horizontal parallax 
is 1" is at a distance 206,265 times the earth's radius; if the 
parallax is 10" it is only ^ as far away, and so on. 



§148] 



DETERMINING THE MOON S PARALLAX. 



95 



Since the radius of the earth varies slightly in different latitudes, 
we take the equatorial radius as a standard, and the equatorial horizon- 
tal parallax is the earth's equatorial semi-diameter as seen from the 
body. It is this which is usually meant when we speak simply of 
" the parallax " of the moon, of the sun, or of a planet ; (but never 
when we speak of the parallax of a star.) 

149. Method of Determining the Moon's Parallax and Dis- 
tance. — We limit ourselves to giving a single one, perhaps the sim- 
plest, of the different methods that are practically available. At each 
of two observatories, B and C, Fig. 30, on. or very nearly on, the 
same meridian and very far apart (Santiago, and Cambridge, U.S., 
for instance), the moon's zenith distance, ZBM and Z'CM, is ob- 
served simultaneously with 
the meridian circle or some 
equivalent instrument. This 
gives in the quadrilateral 
BO CM the two angles OBM 
and OCM, each of which is 
the supplement of the moon's 
geocentric zenith distance at 
B and C respectively. The 
angle BOC, at the centre of 
the earth, is the difference 
of the geocentric latitudes of 
the two observatories (numeri- 
cally, their sum). 

Moreover, the sides BO and CO are known, being radii of the earth. 
The quadrilateral can, therefore, be solved by a simple trigonometrical 
process, 1 and we can find the line MO. Knowing MO and OR, the 
radius of the earth, the horizontal parallax, OMK, follows at once. 

1 The solution is effected as follows : (1) In the triangle BOC, we have 
given BO, OC, and the included angle BOC. Hence we can find the side 
BC, and the two angles OBC and OCB. (2) In the triangle BCM, BC 
is now known, and the two angles MBC and MCB are got by simply sub- 
tracting OBC from OBM, and OCB from OCM: hence we can find BM 
and CM. (3) In the triangle OBM, we know OB, BM, and the included 
angle OBM, from which we can find OM, the moon's distance from tlip 
centre of the earth. 




Fig. 30. — Determination of the Moon's Parallax. 



96 



PABALLAX, DISTANCE, AND VELOCITY. 



[§150 



. 



150. Parallax, Distance, and Velocity of the Moon. — The 

moon's equatorial horizontal parallax is found to average 
3422".0 (57' 2".0), according to Neison, but varies consider- 
ably on account of the eccentricity of the orbit. With this 
value of the parallax we find that the moon's average distance 
from the earth is about 60.3 times the earth's equatorial 
radius, or 238,840 miles, with an uncertainty of perhaps 20 
miles. 

The maximum and minimum values of the moon's distance are 
given by Neison as 252,972 and 221,614. It will be noted that the 
average distance is not the mean of the two extreme distances. 

Knowing the size and form of the moon's orbit, the velocity 
of her motion is easily computed. It averages 2287 miles an 
hour, or about 3350 feet per second. Her apparent angular 
velocity among the stars is about 33 ' an hour on the average, 
which is just a little greater than the apparent diameter of the 
moon itself. 




Fig. 31. — Moon's Path relative to the Sun. 




u 




Fm. 32. Fig. 33. 

Erroneous Representations of the Moon's Path. 



151. Form of the Moon's Orbit with Reference to the Sun. — 

While the moon moves in a small oval orbit around the earth, 
it also moves around the sun in company with the earth. This 



- 



§ 151] DIAMETER, ETC., OF THE MOON. 97 

common motion of the moon and earth, of course, does not 
affect their relative motion, but to an observer outside the 
system, the moon's motion around the earth would be only a 
very small component of the moon's whole motion as seen 
by him. 

The distance of the moon from the earth is only about -^ 
part of the distance of the sun. ,The speed of the earth in its 
orbit around the sun is also more than thirty times greater 
than that of the moon in its orbit around the earth ; for the 
moon, therefore, the resulting path in space is one which is 
always concave towards the sun, as shown in Fig. 31, and not 
like Figs. 32 and 33. 

If we represent the orbit of the earth by a circle having a radius of 
100 inches (8 feet, 4 inches), the moon would deviate from it by only 
one-quarter of an inch on each side, crossing it 25 times in one 
revolution, i.e., in a year. 

152. Diameter, Area, and Bulk of the Moon. — The mean ap- 
parent diameter of the moon is 31' 7". Knowing its distance, 
we easily compute from this by the formula of Art. 12 its real 
diameter, which comes out 2163 miles. This is 0.273 of the 
earth's diameter. 

Since the surfaces of globes vary as the squares of their 
diameters, and their volumes as the cubes, this makes the sur- 
face area of the moon equal to about y 1 ^ of the earth's, and the 
volume (or bulk) almost exactly -^ of the earth's. 

No other satellite is nearly as large as the moon in comparison with 
its primary planet. The earth and moon together, as seen from a 
distance, are really in many respects more like a double planet than 
like a planet and satellite of ordinary proportions. At a time, for 
instance, when Venus happens to be nearest the earth (at a distance 
of about twenty-five millions of miles) her inhabitants would see the 
earth about twice as brilliant as Venus herself at her best appears to 
us, and the moon would be about as bright as Sirius, oscillating back- 
wards and forwards about half a degree each side of the earth. 



98 MASS, DENSITY, AND GRAVITY. [§ 153 

153. Mass, Density, and Superficial Gravity of the Moon. — 

Her mass is about g^ of the earth's mass, (0.0123). 

The accurate determination of the moon's mass is practically an 
extremely difficult problem. Though she is the nearest of all the 
heavenly bodies, it is far more difficult to " weigh " her than to weigh 
Neptune, the remotest of the planets. For the different methods of 
dealing with the problem, we must refer the reader to the " General 
Astronomy" (Art. 243), merely saying that one of the methods is 
by comparing the relative influences of the moon and of the sun in 
raising the tides. 

JYlass 

Since the density of a body is equal to —— , the density 

Volume 

of the moon as compared with that of the earth is found to be 
0.613, or about 3.4 the density of water (the earth's density 
being 5.58). This is a little above the average density of the 
rocks which compose the crust of the earth. This small density 
of the moon is not surprising nor at all inconsistent with the 
belief that it once formed a part of the same mass with the 
earth, since if such were the case the moon was probably 
formed by the separation of the outer portions of that mass, 
which would be likely to have a smaller specific gravity than 
the rest. 

The superficial gravity, or the attraction of the moon for 
bodies at its surface, is about one-sixth that at the surface of 
the earth. That is, a body which w r eighs six pounds on the 
earth's surface would at the surface of the moon weigh only 
one pound (by a spring balance). This is a fact that must be 
borne in mind in connection with the enormous scale of the 
surface structure of the moon. Volcanic forces on the moon 
would throw ejected materials to a vastly greater distance 
than on the earth. 

154. Rotation of the Moon. — The moon rotates on its axis 
once a month, in exactly the same time as that occupied by its 
revolution around the earth ; its day and night are, therefore, 



§ 154 3 LIBRATIONS. 99 

each nearly a fortnight in length, and in the long run it 
keeps the same side always towards the earth: we see to-day 
precisely the same aspect of the moon as Galileo did when he 
first looked at it with his telescope, and the same will con- 
tinue to be the case for thousands of years, if not forever. 

It is difficult for some to see why a mo- 
tion of this sort should be considered a A ( ) 
rotation of the moon, since it is essentially V\T ^~| 
like the motion of a ball carried on a re- 
volving crank (Fig. 34). "Such, a ball/' 
they say, "revolves around the shaft, but 
does not rotate on its own axis." It does 
rotate, however : if we mark one side of the 
ball, we shall find the marked side presented ^ 
successively to every point of the compass FlG . 34# 
as the crank turns, so that the ball turns on 
its own axis as really as if it were whirling upon a pin fastened 
to the table. 

By virtue of its connection with the crank, the ball has two distinct 
motions, (1) the motion of translation, which carries its centre in a circle 
around the axis of the shaft; (2) an additional motion of rotation 1 around 
a line drawn through its centre of gravity parallel to the shaft. But the 
pin A (in the figure) and the hole in which the pin fits, both also turn at 
the same rate, so that the ball does not turn on the pin ; nor the pin, in 
the hole. 

155. Librations. — While in the "long run" the moon keeps 
the same face towards the earth, it is not so in the " short 
run": there is no crank-connection between them. With 
reference to the centre of the earth the moon is continually 
oscillating a little, and these oscillations constitute what 
are called librations, of which we distinguish three ; — viz., the 

1 The motion known as " rotation " consists essentially in this : That a 
line connecting any two points not in the axis of the rotating body, and 
produced to the sky, will sweep out a circle on the celestial sphere. 



100 LIBRATIONS. [§ 155 

libration in latitude, the libration in longitude, and the diurnal 
libration. 

The libration in latitude is due to the fact that the moon's equator 
does not coincide with the plane of its orbit, but makes with it an 
angle of about 62 . This inclination of the moon's equator causes its 
north pole at one time in the month to be tipped a little towards the 
earth, while a fortnight later the south pole is similarly inclined 
towards us. 

Moreover, since the moon's angular motion in its oval orbit is 
variable, while the motion of rotation is uniform like that of any 
other ball, the two motions do not keep pace exactly during the 
month, and we see alternately a few degrees around the eastern and 
ivestern edges of the lunar globe. This is the libration in longitude, 
and amounts to about 7|°. 

Then again when the moon is rising we look over its upper, which 
is then its western edge, seeing a little more of that part of the moon 
than if we were observing it from the centre of the earth. When it 
is setting we overlook in the same way its eastern edge. This con- 
stitutes the so-called diurnal libration, and amounts to about 1°. 
Strictly speaking, this diurnal libration is not a libration of the moon 
at all, but of the observer. The effect is the same, however, as that 
of a true libration. 

Altogether, owing to librations, we see considerably more 
than half the moon's surface at one time or another. About 
41 per cent of it is always visible, 41 per cent never visible, 
and a belt at the edge of the moon covering about 18 per cent 
is rendered alternately visible and invisible by the librations. 

156. The Phases of the Moon. — Since the moon is an opaque 
body shining merely by reflected light, we can see only that 
hemisphere of her surface which happens to be illuminated, 
and of this hemisphere only that portion which happens 
to be turned towards the earth. When the moon is between 
the earth and the sun (at new moon) the dark side is then 
presented directly towards us, and the moon is entirely invisi- 
ble. A week later,, at the end of the first quarter, half of the 



§ 156] 



PHASES OF THE MOON. 



101 



illuminated hemisphere is visible, and we have the half moon 
just as we do a week after the full. Between the new moon 
and the half moon, during the first and last quarters of the 
lunation, we see less than half of the illuminated portion, and 
then have the "crescent" phase. Between half moon and the 
full moon, during the second and third quarters of the luna- 
tion, we see more than half of the moon's illuminated side, 
and have then what is called the "gibbous" phase. 




Fig. 35. — The Moon's Phases. 



Fig. 35 (in which the light is supposed to come from a point far 
above the circle which represents the moon's orbit) shows the way in 
which the phases are distributed through the month. 



102 EARTH-SHINE ON THE MOON. [§ 157 

157. The line which separates the dark portion of the disc from 
the bright is called the " terminator" and is always a semi-ellipse, since 
it is a semi-circle viewed obliquely. The illuminated portion of the 
moon's disc is, therefore, always a figure which is made up of a semi- 
circle plus or minus a semi-ellipse, 1 as shown in Fig. 36 A. It is some- 
times incorrectly attempted to represent the crescent form by a con- 
struction like 36 i>, in which a smaller circle has a portion cut out of 
it by an arc of a larger one. 

It is to be noticed also that ab. the line 
ct 
jsfT\ /"^VX wn ^ cn joins the " cusps" or points of the 

^f J \ \_ p I \ \ crescent, is always perpendicular to a line 
\ \ J C / \ / / drawn f r om the moon to the sun, so that the 

^M-' ^ — LS horns are always turned away from the sun. 

* 22 The precise position, therefore, in which 

p IG# 36# they will stand at any time is perfectly pre- 

dictable, and has nothing whatever to do with 
the weather. Artists are sometimes careless in the manner in which 
they introduce the moon into landscapes. One occasionally sees the 
moon near the horizon w r ith the horns turned downwards, a piece of 
perspective fit to go with Hogarth's barrel, which showed both its 
heads at once. 

158. Earth-Shine on the Moon. — Near the time of new 
moon the whole disc is easily visible, the portion on which 
sunlight does not fall being illuminated by a pale reddish 
light. This light is earth-shine, the earth as seen from the 
moon being then nearly full. 

Seen from the moon, the earth would show all the phases that the 
moon does, the earth's phase being in every case exactly supplementary 
to that of the moon as seen by us at the time. Taking everything 
into account, the earth-shine by which the moon is illuminated near 
new moon is probably from 15 to 20 times as strong as the light of 
the full moon. The ruddy color is due to the fact that the light sent 
to the moon from the earth has passed twice through our atmosphere, 
and so has acquired the sunset tinge. 

1 At new moon or full moon the semi-ellipse of course becomes a semi- 
circle. 






§ 159] CHARACTERISTICS OF THE MOON. 103 



PHYSICAL CHARACTERISTICS OF THE MOON. 

159. The Moon's Atmosphere. — The moon's atmosphere, if 
any exists,, is extremely rare, probably not producing at the 
moon's surface a barometric pressure to exceed -^ of an inch 
of mercury, or y^ of the atmospheric pressure at the earth's 
surface. The evidence on this point is twofold : First, the 
telescopic appearance. 

The parts of the moon near the edge of the disc or " limb " which, 
if there were any atmosphere, would be seen through its greatest pos- 
sible depth, are visible without the least distortion. There is no haze, 
and all the shadows are perfectly black ; there is no sensible twilight 
at the cusps of the moon, and no evidence of clouds or storms, or of 
anything like the ordinary phenomena of the terrestrial atmosphere. 

Second, the absence of refraction, when the moon intervenes 
between us and any more distant object. 

At an eclipse of the sun there is no distortion of the sun's limb 
where the moon cuts it. When the moon " occults " a star, there is 
no distortion or discoloration of the star disc, but both the disappear- 
ance and reappearance are practically instantaneous. Moreover, an 
atmosphere of even slight density, quite insufficient to produce any 
sensible distortion of the image, would notably diminish the time dur- 
ing which the star would be concealed behind the moon, since the 
refraction would bend the rays from the star around the edge of the 
moon so as to render it visible both after it had really passed behind 
the limb and before it emerged from it. 

160. Water on the Moon's Surface. — Of course, if there is 
no atmosphere there can be no liquid water, since the water 
would immediately evaporate and form an atmosphere of vapor 
if no air were present. It is not impossible, however, nor per- 
haps improbable that solid water, i.e., ice and snow, may exist 
on the moon's surface at a temperature too low to liberate va- 
por in quantity sufficient to make an atmosphere dense enough 
to be observable from the earth. 



104 THE MOON'S AIR AND WATER. [§ 161 

161. What has become of the Moon's Air and Water? — 

If the moon ever formed a part of the same mass as the earth, she 
must once have had both air and water. There are a number of pos- 
sible, and more or less probable, hypotheses to account for their disap- 
pearance. (1) The air and water may have struck m, — partly 
absorbed by porous rocks, and partly disposed of in cavities left by 
volcanic action ; partly also, perhaps, by chemical combinations 
and occlusion when the internal temperature became low enough. 
(2) The atmosphere may have flown away ; — and this is perhaps the 
most probable hypothesis. If the " kinetic " theory of gases is true, 
no body of small mass, not extremely cold, can permanently retain 
any considerable atmosphere. A particle leaving the moon with a 
speed exceeding a mile and a half a second would never return. If 
she was ever warm, the molecules of her atmosphere must have been 
continually acquiring velocities greater than this, and deserting her 
one by one. See Physics, pages 270, 271. 

In whatever way, however, it came about, it is quite certain that at 
present no substances that are gaseous or vaporous at low tempera- 
tures exist in any considerable quantity on the moon's surface, — at 
least not on our side of it. 

162. The Moon's Light. — As to quality, it is simply sun- 
light, showing a spectrum identical in every detail with that 
of light coming directly from the sun itself; and this may 
be noted incidentally as an evidence of the absence of a lunar 
atmosphere, which, if it existed, would produce peculiar lines 
of its own in the spectrum. 

The brightness of full moonlight as compared with sunlight 
is about -g-o-oVoir : according to this, if the whole visible hemi- 
sphere were packed with full moons, we should receive from 
it about one-eighth part of the light of the sun. 

Moonlight is not easy to measure, and different experimenters have 
found results for the ratio between the light of the full moon and 
sunlight, ranging all the way from ^ooo (Bouguer) to ^Vou (Wol- 
laston). The value now generally accepted is that determined by 
Zollner, viz., 618 W 



§ l62 l HEAT OF THE MOON. 105 

The half moon does not give, even nearly, half as much 
light as the full moon : near the full the brightness suddenly 
and greatly increases, probably because at any time except at 
the full moon, the moon's visible surface is more or less dark- 
ened by shadows. 

The average albedo or reflecting power of the moon's sur- 
face Zollner states as 0.174; i.e., the moon's surface reflects 
a little more than ± part of the light that falls upon it. 

This corresponds to the reflecting power of a rather light-colored 
sandstone, and agrees well with the estimate of Sir John Herschel, 
who found the moon to be very exactly of the same brightness as the 
rock of Table Mountain when she was setting behind it. There are, 
however, great differences in the brightness of the different portions of 
the moon's surface. Some spots are nearly as white as snow or salt, 
and others as dark as slate. 

163. Heat of the Moon. — For a long time it was impossible 
to detect the moon's heat by observation. Even when concen- 
trated by a large lens, it is too feeble to be shown by the most 
delicate thermometer. The first sensible evidence of it was 
obtained by Melloni in 1846, with the newly invented u thermo- 
pile," by a series of observations from the summit of Vesuvius. 

With modern apparatus it is easy enough to perceive the heat . 
of lunar radiation, but the measurements are extremely difficult. 
A considerable percentage of the lunar heat seems to be heat 
simply reflected like light, while the rest, perhaps three-quarters 
of the whole, is "obscure heat" ; i.e., heat which has first been 
absorbed by the moon's surface and then radiated, like the 
heat from a brick surface that has been warmed by sunshine. 
This is shown by the fact that a comparatively thin plate of 
glass cuts off some 86 per cent of the moon's heat. 

The total amount of heat radiated by the full moon to the earth is 
estimated by Lord Rosse at about one eighty thousandth part of that 
sent us by the sun; but this estimate is probably too high : Prof. 
C. C. Hutchins in 1888 found it TJZ \^. 



106 TEMPERATURE OF THE MOON'S SURFACE. [§ 161 

164. Temperature of the Moon's Surface. — As to the tem- 
perature of the moon's surface, it is difficult to affirm much 
with certainty. On the one hand the lunar rocks are exposed 
to the sun's rays in a cloudless sky for 14 days at a time, so 
that if they were protected by air like the rocks upon the 
earth they would certainly become intensely heated. During 
the long lunar night of 14 clays, the temperature must inev- 
itably fall appallingly low, perhaps 200° below zero. 

Probably the temperature keeps below the freezing-point of water, 
as is the case on our higher mountain tops where there is perpetual 
ice. This falls in with the fact that Langley's bolometer 1 shows the 
presence in the lunar radiations of a considerable percentage of heat- 
rays with a wave-length greater than that radiated from a block of 
ice, and therefore presumably coming from a surface colder than ice. 

Lord Rosse has also found that during a total eclipse of the moon 
her heat-radiation practically vanishes, and does not regain its normal 
value until some hours after she has left the earth's shadow. This 
seems to indicate that she loses heat nearly as fast as it is received, 
and so can never get very warm. 

165. Lunar Influences on the Earth. — The moon's attraction 
co-operates with that of the sun in producing the tides, to be 
considered later. 

There are also certain distinctly ascertained disturbances of 
terrestrial magnetism connected with the approach and reces- 
sion of the moon at perigee and apogee ; and this ends the 
chapter of ascertained lunar influences. 

The multitude of current beliefs as to the controlling influ- 
ence of the moon's phases and changes upon the weather and 
the various conditions of life are mostly unfounded. 

It is quite certain that if the moon has any influence at all of the 
sort imagined, it is extremely slight; so slight that it has not yet been 
demonstrated, though numerous investigations have been made ex- 

1 An instrument for measuring extremely minute quantities of heat 
See "General Astronomy," Art. 343. 



§ 165] MOON'S TELESCOPIC APPEARANCE. 107 

pressly for the purpose of detecting it. We have never been able to 
ascertain with certainty, for instance, whether it is warmer or not, or 
less cloudy or not, at the time of full moon. Different investigations 
lead to contradictory results. 

166. The Moon's Telescopic Appearance and Surface. — Even 
to the naked eye the moon is a beautiful object, diversified 
with markings which are associated with numerous popular 
superstitions. To a powerful telescope these markings mostly 
vanish, and are replaced by a countless multitude of smaller 
details which make the moon, on the whole, the finest of all 
telescopic objects, — especially so to instruments of a moder- 
ate size (say from six to ten inches in diameter) which gener- 
ally give a more pleasing view of our satellite than instruments 
either much larger or much smaller. 

An instrument of this size, with magnifying powers betw r een 
250 and 500, virtually brings the moon within a distance rang- 
ing from 1000 to 500 miles, and since an object half a mile in 
diameter on the moon subtends an angle of about 0".43, it would 
be distinctly visible. A long line or streak even less than a 
quarter of a mile across can probably be seen. With larger 
telescopes the pow r er can now and then be carried at least twice 
as high, and correspondingly smaller details made out, when the 
air is at its best. 

For most purposes the best time to look at the moon is when it is 
between six and ten days old. At the time of full moon few objects 
on the surface are w r ell seen. 

It is evident that while with the telescope we should be able to see 
such objects as lakes, rivers, forests, and great cities, if they existed 
on the moon, it would be hopeless to expect to distinguish any of the 
minor indications of life, such as buildings or roads. 

167. The Moon's Surface Structure. — The moon's surface 
for the most part is extremely broken. With us the moun- 
tains are mostly in long ranges, like the Andes and Himalayas. 
On the moon, the ranges are few in number; but, on the other 
hand, the surface is pitted all over with great " craters" which 



108 



MOON S SUKFACE STRUCTURE. 



[§167 



resemble very closely the volcanic craters on the earth's sur- 
face, though on an immensely greater scale. The largest ter- 
restrial craters do not exceed six or seven miles in diameter; 
many of those on the moon are fifty or sixty miles across, and 
some have a diameter of more than 100 miles, while smaller 
ones from five to twenty miles in diameter are counted by the 
hundred. 

The normal lunar crater (Fig. 37) is nearly circular, sur- 
rounded by a ring of mountains which rise anywhere from a* 
thousand to twenty thousand feet above the surrounding coun- 
try. The floor with- 
in the ring may be 
either above or be- 
low the outside lev- 
el; some craters are 
deep, and some are 
filled nearly to the 
brim. In a few 
cases the surround- 
ing mountain ring 
is entirely absent, 
and the crater is a 
mere hole in the plain. Frequently in the centre of the crater 
there rises a group of peaks, which attain about the same ele- 
vation as the encircling ring, and these central peaks often 
show holes or minute craters in their summits. 




Fig. 37. — A Normal Lunar Crater (Nasmyth). 



On some portions of the moon these craters stand very thickly ; 
older craters have been encroached upon or more or less completely 
obliterated by the newer, so that the whole surface is a chaos of 
which the counterpart is hardly to be found on the earth, even in the 
roughest portions of the Alps. This is especially the case near the 
moon's south pole. It is noticeable, also, that, as on the earth 
the youngest mountains are generally the highest, so on the moon 
the more newly formed craters are generally deeper and more precip- 
itous than the older. 



§167] 



OTHER LUNAR FORMATIONS. 



109 



The height of a lunar mountain or depth of a crater can be 
measured with considerable accuracy by means of its shadow ; 
or in the case of a mountain, by the measured distance between 
its summit and the 
u terminator " (Art. 
157), at the time when 
the top first catches 
the light and looks 
like a star quite de- 
tached from the bright 
part of the moon, as 
seen in Fig. 38. 

168. The striking re- 
semblance of these for- 
mations to terrestrial 
volcanic structures, like 
those exemplified by Ve- 
suvius and others, makes 
it natural to assume that 
they had a similar origin . 
This, however, is hot ab- 
solutely certain, for there 
are considerable difficul- 
ties in the way, espe- 
cially in the case of what are called the great " Bulwark Plains." 
These are so extensive that a person standing, in the centre could not 
even see the summit of the surrounding ring at any point ; and yet 
there is no line of demarcation between them and the smaller craters, 
— the series is continuous. Moreover, on the earth, volcanoes neces- 
sarily require the action of air and water, which do not at present 
exist on the moon. It is obvious, therefore, that if these lunar craters 
are the result of volcanic eruptions, they must be, so to speak, "fossil" 
formations, for it is quite certain that there is absolutely no evidence of 
present volcanic activity. 

169. Other Lunar Formations. — The craters and mountains 
are not the only interesting formations on the moon's surface. 




Fig. 38.— Gassendi (Nasmyth). 



110 



OTHER LUNAR FORMATIONS. 



[§169 



There are many deep, narrow, crooked valleys that go by the 
name of "rills" some of which may once have been water- 
courses. Fig. 39 shows several of them. Then there are 
numerous straight " clefts" half a mile or so wide and of un- 
known depth, running 
in some cases several 
hundred miles, straight 
through mountain and 
valley, without any ap- 
parent regard for the 
accidents of the sur- 
face ; they seem to be 
deep cracks in the crust 
of our satellite. Most 
curious of all are the 
light-colored streaks or 
"rays" which radiate 
from certain of the cra- 
ters, extending in some 
cases a distance of 
many hundred miles. 
These are usually from 
five to ten miles wide, 
and neither elevated 
or depressed to any considerable extent with reference to the 
general surface. Like the clefts, they pass across valley and 
mountain, and sometimes through craters, without any change 
in width or color. No thoroughly satisfactory explanation has 
ever been given, though they have been ascribed to a staining of 
the surface by vapors ascending from rifts too narrow to be visible. 

The most remarkable of these "ray systems " is the one connected 
with the great crater Tycho, not very far from the moon's south 
pole. The rays are not very conspicuous until within a few days 
of full moon, but at that time they and the crater from which they 
diverge constitute by far the most striking feature of the whole lunar 
surface. 




Fig. 3J. — Archimedes and the Apennines (Nasmyth). 



§ 170] LUNAR MAPS. Ill 

170. Lunar Maps. — A number of maps of the moon have been 
constructed by different observers. The most recent and extensive is 
that by Schmidt of Athens, on a scale 7 feet in diameter : it was pub- 
lished by the Prussian government in 1878. Of the smaller maps 
available for ordinary lunar observation, perhaps the best is that giren 
in Webb's " Celestial Objects for Common Telescopes." Two new 
photographic, large-scale, lunar maps are now (1897) being published, 
by the Lick and Paris observatories. 

171. Lunar Nomenclature. — The great plains upon the moon's 
surface were called by Galileo "oceans" or " seas " (Maria), for he 
supposed that these grayish surfaces, which are visible to the naked 
eye and conspicuous in a small telescope, though not with a large one, 
were covered with water. 

The ten mountain ranges on the moon are mostly named after ter- 
restrial mountains, as Caucasus, Alps, Apennines, though two or three 
bear the names of astronomers, like Leibnitz, Doerfel, etc. 

The conspicuous abaters bear the names of eminent ancient and 
mediaeval astronomers and philosophers, as Plato, Archimedes, Tycho, 
Copernicus, Kepler, and Gassendi ; while hundreds of smaller and less 
conspicuous formations bear the names of more modern astronomers. 

This system of nomenclature seems to have originated with Kicci- 
oli, who made the first map of the moon in 1650. 

172. Changes on the Moon. — It is certain that there are no 
conspicuous changes, — there are no such transformations as 
would be presented by the earth viewed telescopically, — no 
clouds, no storms, no snow of winter, and no spread of vege- 
tation in the spring. At the same time, it is confidently main- 
tained by some observers that here and there alterations do 
take place in the details of the lunar surface, while others as 
stoutly dispute it. 

The difficulty in settling the question arises from the great changes 
in the appearance of a lunar object under varying illumination. To 
insure certainty in such delicate observations, comparisons must be 
made between the appearance of the object in question, as seen at 
precisely the same phase of the moon, with telescopes (and eyes too) of 
equal power, and under substantially the same conditions in other 



112 



LUNAR MAPS. 



[§172 



respects, such as the height of the moon above the horizon, and the 
clearness and steadiness of the air. It is, of course, very difficult to 
secure such identity of conditions. (For an account of certain sup- 
posed changes, see Webb's " Celestial Objects.") 

173. Fig. 40 is reduced from a skeleton map of the moon by 
Neisom and though not large enough to exhibit much detail, 
will enable a student with a small telescope to identify the 
principal objects by the help of the key. 



KEY TO THE PKINCIPAL OBJECTS INDICATED IN FIG. 40. 



A. Mare Humorum. 




K. 


Mare 


Nubium. 


B. Mare Nectaris. 




L. 


Mare 


Frigoris. 


C. Oceanus Procellarum. 


T. 


Leibnitz Mountains. 


D. Mare Fecunditatis 




U. 


Doerfel Mountains. 


E. Mare Tranquilitatis. 


V. 


Rook Mountains. 


F. Mare Crisium. 




W. 


D'Alembert Mountains. 


G. Mare Serenitatis. 




X. 


Apennines. 


H. Mare Imbrium. 




F. 


Caucasus. 


/. Sinus Iridum. 




Z. 


Alps. 




1. Clavius. 


14. 


Alphonsus. 




27. Eratosthenes, 


2. Schiller. 


15. 


Theophilus. 




28. Proclus. 


3. Maginus. 


16. 


Ptolemy. 




28'. Pliny. 


4. Schickard. 


17. 


Langrenus. 




29. Aristarchus. 


5. Tycho. 


18. 


Hipparchus. 




30. Herodotus. 


6. Walther. 


19. 


Grimaldi. 




31. Archimedes. 


7. Purbach. 


20. 


Flams teed. 




32. Cleomedes. 


8. Petavius. 


21. 


Messier. 




33. Aristillus. 


9. " The Railway." 


22. 


Maskelyne. 




34. Eudoxus. 


10. Arzachel. 


23. 


Triesnecker. 




35. Plato. 


11. Gassendi. 


24. 


Kepler. 




36. Aristotle. 


12. Catherina. 


25. 


Copernicus. 




37. Endymion. 


13. Cyrillus. 


26. 


Stadius. 







174. Lunar Photography. — It is probable that the question of 
changes upon the moon's surface will soon be authoritatively decided 
by means of photography. The earliest success in lunar photography 
was that of Bond of Cambridge (U.S.), in 1850, using the old 



§174] 



LUNAK PHOTOGRAPHY. 



113 



Daguerreotype process. This was followed by the work of De la Rue 
in England, and by Dr. Henry Draper and Mr. Rutherfurd in this 
country. Until very recently, Mr. Rutherfurd's pictures have remained 
absolutely unrivalled ; but within the last year or two, plates which 




Fig. 40. — Map of the Moon, reduced from Neison. 

have been taken at Cambridge, U. S., and at the Lick Observatory, 
as well as by Mr. Common in England and the Henry brothers at 
Paris, are far in advance even of the best of Rutherfurd's, showing 
such craters as Copernicus and Ptolemy with a diameter of two or 
three inches ; i.e., on a scale larger than that of Schmidt's map. 



114 THE SUN. [§ 175 



CHAPTER VI. 

THE SUN. — ITS DISTANCE, DIMENSIONS, MASS, AND 
DENSITY. — ITS ROTATION AND EQUATORIAL ACCEL- 
ERATION. METHODS OF STUDYING ITS SURFACE. — 

SUN SPOTS. — THEIR NATURE, DIMENSIONS, DEVELOP- 
MENT, AND MOTIONS. THEIR DISTRIBUTION AND 

PERIODICITY. — SUN-SPOT THEORIES. 

The sun is the nearest of the stars; a hot, self-luminous 
globe, enormous as compared with the earth and moon, though 
probably only of medium size among its peers ; but to the earth 
and the other planets which circle around it, it is the grandest 
and most important of all the heavenly bodies. Its attraction 
controls their motions, and its rays supply the energy which 
maintains every form of activity upon their surfaces. 

175. The Sun's Distance. — Its distance maybe determined 
by finding its horizontal parallax (Art. 147); i.e., the semi- 
diameter of the earth as seen from the sun. The mean value of 
this parallax is very near 8".80, with a probable error certainly 
less than ± 0".01. The distance may also be ascertained by 
measuring experimentally the velocity of light, and combining 
this with the so-called " Constant of Aberration " (Art. 127), 
or with the time required by light to travel from the sun to the 
earth, as deduced from the observation of the eclipses of Ju- 
piter's satellites (Art. 355). 

We reserve for the Appendix the discussion of the principal 
methods by which the parallax has been determined. 



ii 



§ 175] DIMENSIONS OF THE SUN. 115 

Taking the horizontal parallax at 8".8, the mean distance of 
the sun (a being the earth's equatorial radius) equals 

a x 2( g26 g = 23439 x a. (See Art. 148.) 

With Clark's value of a (Art. 84), this gives 149,500,000 kilo- 
metres, or 92,897,000 miles, which, however, is uncertain by 
at least 50,000 miles. The distance is variable, also, to the 
extent of about 3,000,000 miles, on account of the eccentricity 
of the earth's orbit, the earth being nearer the sun in December 
than in June. 

Knowing the distance of the sun, the orbital velocity of the 
earth is easily found by dividing the circumference of the orbit 
by the number of seconds in a sidereal year. It comes out 
18.495 miles per second. (Compare this with the velocity of a 
cannon-ball — seldom exceeding 2000 feet per second.) 

This distance is so much greater than any with which we have to 
do on the earth, that it is impossible to reach a conception of it except 
by illustrations. Perhaps the simplest is that drawn from the motion 
of a railway train, which, going a thousand miles a day (nearly 42 
miles an hour without stops), would take 254 J years to make the 
journey. If sound were transmitted through interplanetary space, 
and at the same rate as through our own atmosphere, it would make 
the passage in about 14 years ; i.e., an explosion on the sun would be 
heard by us 14 years after it actually occurred. Light traverses the 
distance in 499 seconds. 

176. Dimensions of the Sun. — The sun's mean apparent 
diameter is 32' 4" ±2". Since at the distance of the sun, one 
second equals 450.36 miles, its diameter l is 866,500 miles, or 
109^- times that of the earth. 

If we suppose the sun to be hollowed out, and the earth 
placed at the centre, the sun's surface would be 433,000 miles 

1 It is quite possible that the sun's diameter is variable to the extent of 
a few hundred miles, since the sun is not solid. 



116 



DIMENSIONS OF THE SUN. 



[§176 



away. Now, since the distance of the moon is about 239,000 
miles, she would be only a little more than half-way out from 
the earth to the inner surface of the hollow globe, which would 
thus form a very good background for the study of the lunar 
motions. Fig. 41 illustrates the size of the sun and of such 




Fig. 41. — Dimensions of the Sun compared with the Moon's Orbit. 

objects upon it as the sun spots and prominences, as compared 
with the size of the earth and of the moon's orbit. 

If we represent the sun by a globe two feet in diameter, the 
earth on that scale would be 0.22 of an inch in diameter, the 
size of a very small pea. Its distance from the sun would be 
just about 220 feet, and the nearest star, still on the same scale, 
would be 8000 miles away at the antipodes. 

As a help to the memory, it is worth noticing that the sun's diam- 
eter exceeds the earth's just as many times as it is itself exceeded by 
the radius of the earth's orbit. Its diameter is nearly 110 times that 
of the earth, and it is also, roughly, the 110th part of its distance 
from us. 



§ 176] THE SUN'S MASS. 117 

Since the surfaces of globes are proportional to the squares 
of their radii, the surface of the sun exceeds that of the earth 
in the ratio of 109.5 2 : 1 ; i.e., the area of its surface is about 
12,000 times the surface of the earth. 

The volumes of spheres are proportional to the cubes of their 
radii. Hence, the sun's volume or bulk is 109.5 3 , or 1,300000 
times that of the earth. 

177. The Sun's Mass. — The mass of the sun is very nearly 
332,000 times that of the earth. There are various ways of 
getting at this result. Perhaps for our purpose the most con- 
venient is by comparing the earth's attraction for bodies at her 
surface {i.e., the value of g as determined by pendulum experi- 
ments, Physics, p. 106) with the attraction of the sun for the 
earth, or the central force which keeps her in her orbit. Put 
/ for this force (measured like gravity by the velocity it gen- 
erates in one second), g for the force of gravity (32 feet, 2 
inches per second), r the earth's radius, R the sun's distance, 
and let E and S be the masses of the earth and sun respec- 
tively. Then the law of gravitation gives us the proportion 

J ' g " M 2 ' r 2 ' 

whence, S = E xi — jxl — 

From the size of the earth's orbit (considered as a circle), and 
the length of the year, /is found 1 to be 0.2333 inches. 

Therefore, L = 0.0006044 = — *— nearly. But - = 23,439, 
g 1654 r 

the square of which is 549,387,000, nearly ; whence, 

S = Ex -i- X 549,387,000 = 332,000 E. 
1654 

1 The formula is /= — , V being the velocity of the earth in its 
H 
orbit, 18.495 miles per second. We may also use the equivalent formula, 

f= , T being the length of the vetir in seconds. 

T 2 



118 THE SUN'S DENSITY. [§177 

Wo note in passing that ^expresses the distance which the earth 
falls towards the sun every second ; just as \<j (10 feet) is the distance 
a body at the earth's surface falls in the first second. This quantity, 
If or 0.116 inches, is the amount by which the earth's orbit deviates 
from a straight line in a second. In travelling 18£ miles the deflec- 
tion is only about one-ninth of an inch. 

178. The Sun's Density. — Its density as compared with that 
of the earth may be found by simply dividing its m,ass by its 
volume (both as compared with the earth); i.e., the sun's 
density equals ,'YoVoVo = 0.255, a little more than a quarter of 
the earth's density. 

To get its specific gravity (i.e., its density compared with 
water) we must multiply this by 5.58, the earth's mean spe- 
cific gravity, This gives 1.41. That is, the sun's mean density 
is less than M 2 times that of water, — a very significant re- 
sult as bearing on its physical condition, especially when we 
know that a considerable portion of its mass is composed of 
metals. 

179. Superficial Gravity, or Gravity at the Sun's Surface. — 
This is found by dividing the sun's mass by the square of its 
radius, which gives 27.6; i.e., a body weighing one, pound on 
the earth's surface would there weigh 27.0 pounds, and a per- 
son who weighs L50 pounds here, would there weigh nearly two 
tons. A body would fall 444 feet in a second instead of 16 
feet as here, and a pendulum which vibrates seconds on the 
earth would vibrate in less than one-fifth of a second there. 

180. The Sun's Rotation. — Dark spots are often visible 
Upon the sun's surface, which pass across the disc from east to 
west, and indicate an axial rotation. The average time occu- 
pied by a, spot in passing around the sun and returning to the 
same apparent position as seen from the earth is on the aver- 
age 27.25 days. This interval, however, is not the true or 
sidereal time of the sun's rotation, but the synodic, as is evi- 



180] 



THE SUN S ROTATION. 



119 



T 



1 

E 



1 



*Z5* 



dent from Fig. 42. Suppose an observer on the earth at 
E sees a spot on the centre of the sun's disc at S ; while 
the sun rotates E will also 
move forward in its orbit; 
and the - observer, the next 
time he sees the spot on the 
centre of the disc, will be sf — \s' 

at E\ the spot having gone 
around the whole circumfer- 
ence plus the arc SS'. 

The equation by which the 
true period is deduced from the 
synodic is the same as in the case 
of the moon (Art. 141); viz., 




E — ■—- E 

Fig. 42. 
Synodic and Sidereal Revolution of the Sun. 



T being the true period of the sun's rotation, E the length of the 
year, and & the observed synodic rotation. This gives T= 25.35. 

Different observers, however, get slightly different results. Car- 
rington finds 25.38 ; Spoerer, 25.23. 

The paths of the spots across the sun's disc are usually 
more or less oval, showing that the sun's axis is inclined to the 
ecliptic, and so inclined that the north pole is tipped about 
1\° towards the position that the earth occupies near the 





OEC. MARCH. JUN£. SEPT. 

Fig. 43. — Path of Sun Spots across the Sun's Disc. 

first of September. Twice a year the paths become straight, 
when the earth is in the plane of the sun's equator, — on June 
3d and December 5th. Fi^. 43 illustrates this. 



120 PECULIAK LAW OF THE SUN'S ROTATION. [§ 181 

181. Peculiar Law of the Sun's Rotation. — It was noticed 
quite early that different spots give different results for the 
period of rotation, but the researches of Carrington about 30 
years ago first brought out the fact that the differences are 
systematic, so that at the solar equator the time of rotation is 
less than on either side of it. For spots near the sun's equa- 
tor it is about 25 days ; in solar latitude 30°, 26.5 ; and in 
solar latitude 40°, 27 days. The time of rotation of the 
sun's surface in latitude 45° is fully two days longer than at 
the equator ; but we are unable to follow the law further 
towards the sun's poles, because spots are almost never found 
beyond the parallels of 45°, and there are no other well-defined 
markings by which we can reckon. 

Clearly the sun's visible surface is not solid, but permits motions 
and currents like those of our air and oceans. It might be argued 
that the spots misrepresent the sun's real rotation, not being fixed 
upon its surface ; but the " faculse " (Art. 184) give the same result, 
and so do spectroscopic observations (Art. 200). 

Possibly this equatorial acceleration may be, in some way not yet 
explained, an effect of the tremendous outpour of heat from the solar 
surface ; but more likely, according to the most recent investigations, 
it is a long persisting " survival " from the sun's past history, and 
not attributable to causes now acting. If so, it will gradually die 
out, but it may be thousands or millions of years before it entirely 
disappears. 

182. Arrangements for the Study of the Sun's Surface. — 

The heat and light of the sun are so intense that we cannct 
look directly at it with a telescope as we do at the moon. 

A very convenient method of exhibiting the sun to a number 
of persons at once is simply to attach to a small telescope a 
frame carrying a screen of white paper at a distance of a foot 
or more from the eye-piece, as shown in Fig. 44. With a 
proper adjustment of the focus, a distinct image is formed on 
the screen, which shows the main features very fairly ; indeed 
with proper precautions, almost as well as the most elaborate 



§182] 



PHOTOGRAPHY. 



121 



apparatus. Still, it is generally more satisfactory to look at 
the sun directly with a suitable eye-piece. With a small tele- 
scope, not more than 2\ or 3 inches 
in diameter, it is usual to intro- 
duce a simple shade-glass between 
the eye-piece and the eye, but the 
dark glass soon becomes very hot 
and is apt to crack. With larger 
instruments it is necessary to use 
eye-pieces specially designed for 
the purpose, and known as solar 
eye-pieces, or " Jielioscopes." 




Fig. 44. — Telescope and Screen. 




Fig. 45. — Herschel Eye-Piece. 



wider its image of a sharp line. 

fore, to sacrifice the definition of delicate details. 



The simplest, and a very good one, 
is known as Herschel's, in which the 
sun's rays are reflected at right angles 
by a plane of un silvered glass (Fig. 
45). With this apparatus, although 
the reflected light is still too intense 
for the unprotected eye, only a thin 
shade glass is required, and it does 
not become much heated. It is not 
a good plan to " cap " the object-glass 
in order to cut off part of the light. 
The smaller the object-lens of the 
telescope, the larger the image it 
makes of a luminous point, or the 

To cut dowm the aperture is, there- 



183. Photography. — In the study of the sun's surface, pho- 
tography is for some purposes very advantageous and much 
used. The instrument must, however, have lenses specially 
constructed for photographic operations, since an object-glass 
which w^ould give admirable results for visual purposes would 
be worthless photographically, and vice versa (see Appendix. 



122 THE PHOTOSPHERE. [§ 183 

Art. 534). The disc of the sun on the negatives is usually 
from two to ten inches in diameter, but photographs of small 
portions of the solar surface are often on a very much larger 
scale, as in the remarkable pictures made by Janssen at 
Meudon. 

Photographs have the great advantage of freedom from preposses- 
sion on the part of the observer, and in an instant of time they 
secure a picture of the whole surface of the sun such as would require 
a skilful draughtsman hours to copy. But, on the other hand, they 
take no advantage of the instants of fine seeing ; they represent the 
solar surface as it happened to appear at the moment when the plate 
was uncovered, affected by all the momentary distortions due to 
atmospheric disturbances. 

184. The Photosphere. — The sun's visible surface is called 
the "Photosphere/' i.e., the "light sphere/' and when studied 
under favorable conditions with rather a low magnifying 
power, it appears as a disc considerably darker at the edge 
than in the centre, and not smoothly bright but mottled, look- 
ing much like rough drawing paper. With a powerful instru- 
ment, and the best atmospheric conditions, the surface is seen 
to be made up, as shown in Fig. 46, of a comparatively darkish 
background, sprinkled over with grains or " nodules" as Her- 
schel calls them, of something much more brilliant, — " like 
snow-flakes on gray cloth," according to Langley. These nod- 
ules or " rice grains " are from 400 to 600 miles across, and in 
the finest seeing, themselves break up into more minute "gran- 
ules." For the most part, the nodules are about as broad as 
they are long, though of irregular form ; but here and there, 
especially in the neighborhood of the spots, they are drawn 
out into long streaks, known as " filaments," " willow leaves," 
or " thatch straws." 

Certain bright streaks called "faculce " are also usually visi- 
ble here and there upon the sun's surface, and though not very 
obvious near the centre of the disc, they become conspicuous 



§ 184] SUN SPOTS. 123 

near the " limb," especially in the neighborhood of the spots. 
Very probably they are of the same material as the rest of 




Fkj. 46.— The Great Sun Spot of September, 1870, and the Structure of the Photosphere. 
From a Drawing by Professor Langley. From the " New Astronomy," by permission of 
the Publishers. 

the photosphere, but elevated above the general level, and in- 
tensified in brightness. 



124 



SUN SPOTS. 



[§184 



Fig. 47 shows faculae around a spot near the sun's limb. 
The photosphere is probably a sheet of clouds floating in a 
less luminous atmosphere, just as a cloud formed by the con- 
densation of water-vapor floats in the air. It is intensely 
brilliant, for the same reason that the " mantle " of a Wels- 
bach burner outshines the gas-flame which heats it : the radiat- 
ing power of the solid and liquid particles which compose the 
clouds is extremely high. 




Fig. 47. — Facula^ at Edge of the Sun. (De La Rue.) 



185. Sun Spots. — Sun spots, whenever visible, are the most 
conspicuous and interesting objects upon the solar surface. 
The appearance of a normal sun spot, Fig. 48, fully formed, 
and not yet beginning to break up, is that of a dark central 
"umbra," more or less nearly circular, with a fringing "pe- 
numbra," composed of converging filaments. The umbra itself 
is not uniformly dark throughout, but is overlaid with filmy 
clouds, which usually require a good telescope and helioscope 
to make them visible, but sometimes, though rather infre- 






§185] 



SUN SPOTS. 



125 



quently, are conspicuous, — as in the figure. Usually, also, 
within the umbra there are a number of round and very black 
spots, sometimes called "nucleoli," but often referred to as 
" Dawes' holes " after the name of their first discoverer. 

The darkest portions of the umbra, however, are dark only 
by contrast. Photometric observations show that even the 




Fig. 48. — A Normal Sun Spot. (Secchi; modified.) 

nucleus gives about one per cent as much light as a correspond- 
ing area of the photosphere: the blackest portion of a sun spot 
is really more brilliant than a calcium light. 



Very few spots are strictly normal. They are often gathered in 
groups with a common penumbra, which is partly covered with bril- 
liant "bridges" extending across from the outside photosphere. 
Frequently the umbra is out of the centre of the penumbra, or has a 
penumbra on one side only, and the penumbral filaments, instead of 
converging regularly towards the nucleus, are often distorted in every 
conceivable way. 



126 



thp: suns spots. 



[§186 



186. Nature of Sun Spots. — Until very recently sun spots 
have been believed to be cavities in the photosphere, rilled 
with gases and vapors cooler, and therefore darker, than the 
surrounding region. This theory is founded on the fact that 
many spots as they cross the sun's disc behave as shown in 
Fig. 49. Near the limb they look just as they would if they 
were saucer-shaped hollows, with sloping sides colored gray, 
and the bottom black. 

This theory, however, has lately been seriously called in 
question : many spots, perhaps a majority, as shown by photo- 




Fig. 49. — Sun Spots as Cavities. 

graphs and drawings, do not present the appearances described. 
But the principal objection lies in the behavior of spots in re- 
spect to their heat-radiation. Near the centre of the disc the 
thermopile shows that as they are darker, so also they emit 
much less heat than the photosphere around them ; but near 
the limb the difference becomes less, and in some cases is even 
reversed : a fact most easily explained by supposing the spot 
to be high up above the photosphere. 

On the whole it now seems most probable that different 
spots lie at very different levels : some low down, forming 
hollows in the photosphere, but others at a considerable 
elevation. 

The penumbra is usually composed of "thatch straws/' or 
long drawn out filaments of photospheric cloud, and these, as 
has been said, converge in a general way towards the centre of 
the spot. 



§ 186] DIMENSIONS OF SUN SPOTS. 127 

At its inner edge, the penumbra, from the convergence of these 
filaments, is usually brighter than at the outer. The inner ends of the 
filaments are ordinarily club-formed ; but sometimes they are drawn 
out into fine points, which seem to curve downward into the umbra, 
like the rushes over a pool of water. The outer edge of the penum- 
bra is usually pretty sharply bounded, and there the penumbra is 
darkest. In the neighborhood of the spot, the surrounding photo- 
sphere is usually much disturbed and elevated into facube, as shown 
in Fig. 47. 

187. Dimensions of Sun Spots. — The diameter of the um- 
bra of a sun spot varies all the way from 500 miles in the 
case of a very small one, to 40,000 or 50,000 miles, in the case 
of the largest. The penumbra surrounding a group of spots 
is sometimes 150,000 miles across, though that is an excep- 
tional size. Xot infrequently, sun spots are large enough to 
be visible with the naked eye, and can actually be thus seen at 
sunset or through a fog, or by the help of a colored glass. 

The Chinese have many records of such objects, but the 
real discovery of sun spots dates from 1610, as an immediate 
consequence of Galileo's invention of the telescope. Fabricius 
and Scheiner, however, share the honor with him as being 
independent observers. 

188. Duration, Development, and Changes of Spots. — The 

duration of sun spots is very various ; but they are always 
short-lived phenomena, astronomically speaking, sometimes 
lasting only for a few days, though more frequently for a month 
or two. In a single instance, the life of a spot group reached 
nearly eighteen months. 

According to Secchi, the formation of a spot is usually announced 
some days in advance by a considerable disturbance of the surface of 
the photosphere, and by the formation of faculse with groups of 
" pores," or minute dark points among them. These pores grow larger 
and coalesce, and at the same time the surrounding region takes on 
the filamentary structure of the penumbra, and the umbra finally 



128 MOTIONS OF THE SPOTS. [§ 188 

appears in the centre. The process ordinarily requires several days, 
but sometimes a few hours are sufficient. If the originating dis- 
turbance is particularly violent, it usually results not in a single 
normal spot, but in a group of irregular nuclei scattered within a 
common penumbra, and then the spots themselves usually break up 
into fragments, and these again into others which separate from each 
other with considerable velocity. Moreover, at each new disturbance, 
the forward portions of the group show a tendency to wade forward 
toward the east through the photosphere, leaving behind them a trail 
of smaller spots. 

Occasionally a spot shows a distinct cyclonic motion, the filaments 
being drawn spirally inward ; and in different members of the same 
group of spots, these cyclonic motions are not seldom in opposite 
directions, as of wheels gearing into each other. 

When a spot vanishes, it is usually by the rapid encroachment of 
the photospheric matter, which, as Secchi expresses it, appears to " fall 
pell-mell into the cavity," completely burying it and leaving its place 
covered by a group of faculse. 

189. Motions of the Spots. — Spots within 15° or 20° of the 

sun's equator usually drift slowly towards it, while those in 
the higher latitudes drift away from it; but the motion is slight 
and exceptions are frequent. Spot groups in which the dis- 
turbance is violent, as intimated in the preceding section, seem 
to move towards the east on the sun's surface more rapidly 
than the quiet ones in the same latitude. Within and around 
the spot itself, the motion so far as can be observed, is usually 
inward towards the centre, and there downward. Not infre- 
quently fragments at the inner edge of the penumbral fila- 
ments break off, move towards the centre of the spot, and there 
disappear as if swallowed up by a vortex. 

Occasionally, though seldom, the downward motion at the centre 
of a spot is vigorous enough to be detected by the displacement of 
lines in the spectrum, while around the outer edges of the penumbra 
the same instrument in such cases usually shows a violent up-boiling 
from beneath (see Art. 200). 



§190] 



DISTRIBUTION OF SPOTS. 



129 



190. Distribution of Spots and Periodicity of Sun Spots. — 

It is a significant fact that the spots are confined mostly to 
two zones of the sun's surface between 5° and 40° of north and 
south latitude. A few are found near the equator about the 
time of the spot maximum, and practically none beyond the 
latitude of 45°. Fig. 50 shows the distribution of several 
thousand spots as observed by Sporer and Carrington. 

In 1843, Schwabe of Dessau, by the comparison of an exten- 




Fig. 50. — Distribution of Sun Spots in Latitude. 

sive series of observations then covering nearly twenty years, 
showed that the sun spots are probably periodic, being at some- 
times much more numerous than at others, with a roughly reg- 
ular recurrence every ten or eleven years. A few years later 
he fully established this remarkable result. 



Wolf of Zurich has collected all the observations discoverable, and 
has obtained a pretty complete record back to 1610, from which he 
has constructed the annexed diagram (Fig. 51) in which the ordinates 
represent what he calls his " relative numbers," which may be taken 
as the index of the sun's spottedness. 

The average period is 11.1 years, but the maxima are somewhat 
irregular, both in time and as to the extent of spottedness. The tw r o 



130 



THE CAUSE OF SUN SPOTS. 



[§ 190 



last maxima occurred in 18 So and 1893. During the maximum, the 
surface of the sun is never free from spots, from 25 to 50 being fre- 
quently visible at once. During the minimum, on the contrary, weeks 
and even months pass without the appearance of a single one. The 
cause of this periodicity is not known, but it is probably due to causes 
within the sun itself rather than to anything external. 



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Fig. 51 —. Wolf's Sun-Spot Numbers. 



190*. Another curious and important fact has been brought out 
by Spoerer, though not yet explained. Speaking broadly, the dis- 
turbance which produces the spots of a given period first manifests 
itself in two belts, about 30° north and south of the sun's equator. 
These belts then draw in towards the equator, and the spot-maximum 
occurs when their latitude is about 16° ; while the disturbance finally 
dies out at a latitude of from 5° to 10°, about twelve or fourteen years 
after its first outbreak. Two or three years before this disappearance, 
however, two new zones of disturbance show themselves. Thus at 
the spot-minimum there are usually four well-marked spot-belts : two 
near the sun's equator, due to the expiring disturbance, and two in 
high latitudes, du^ to the newly beginning outbreak. 



§ 1^1] TERRESTRIAL INFLUENCE OF SUN SPOTS. 131 

191. The Cause of Sun Spots. — As to this, very little can be 
said to be really known. Numerous theories more or less satisfactory 
have been proposed. On the whole, perhaps the most probable view 
is that they are the effect of eruptions. Probably, however, they are 
not the holes or " craters " through which the eruptions break out, as 
Secchi at one time maintained, and as Mr. Proctor did to the very last. 
It is more likely, in accordance with Secchi's later view r s, that, when an 
eruption takes place, a 'hollow or "sink" results in the photospheric 
cloud-surface somewhere near it, in which hollow the cooler gases and 
vapors collect. 

Mr. Lockyer is disposed to revive an old theory first suggested by 
Sir John Herschel, viz., that the spots are formed not by any action 
from within, but by cool matter descending from above, — matter very 
likely of meteoric origin ; but it is not easy to reconcile this with the 
peculiar distribution of the spots upon the sun's surface. 

Faye considers them to be solar cyclones somewhat analogous to 
terrestrial storms, and in 1894 E. Oppolzer of Vienna proposed a still 
different meteorological theory, which attributes them to masses of 
gas and vapor which, ascending from the polar regions, drift towards 
the equator and descend in the spot-zones, becoming warmed and 
"dried" by the operation, just as is the case with descending currents 
in the atmosphere of the earth. If he is right, the spots are actually 
hotter than the surrounding photosphere, but less luminous because 
purely gaseous (see Art. 184). 

192. Terrestrial Influence of Sun Spots. — One influence of 
sun spots upon the earth is perfectly demonstrated. When 
the spots are numerous, magnetic disturbances (magnetic storms) 
are most numerous and most violent upon the earth, — a fact 
not to be wondered at, since notable disturbances upon the 
sun's surface have been in many cases immediately followed by 
magnetic storms with brilliant exhibitions of the Aurora Bore- 
alis, as- in 1859 and 1883. The nature and mechanism of the 
connection is as yet unknown, but the fact is beyond doubt. 
The dotted lines in the figure of the sun-spot periodicity rep- 
resent the magnetic storminess of the earth at the indicated 
dates (Fig. 51) ; and the correspondence between these curves 
and the curves of the spottedness makes it impossible to 
question their relation to some common cause. 



132 TERRESTRIAL INFLUENCE OF SUN SPOTS. [§192 

It has been attempted, also, to show that the periodical disturb- 
ance of the sun's surface is accompanied by effects upon the earth's 
meteorology, — upon its temperature, barometric pressure, storminess, 
and the amount of rainfall. On the whole, it can only be said that 
while it is entirely possible that real effects of the sort are produced, 
they must be slight and almost entirely masked by the effect of purely 
terrestrial disturbances. The results obtained by different investiga- 
tions in attempting to co-ordinate sun-spot phenomena with meteor- 
ological phenomena are thus far unsatisfactory and even contradictory. 
We may add that the spots cannot produce any sensible effects by 
their direct action in diminishing the light and heat of the sun. They 
do not directly alter the amount of the solar radiation at any time by 
as much as one part in a thousand. 



[§193 THE SPECTROSCOPE. 133 



CHAPTER VII. 

THE SPECTROSCOPE, THE SOLAR SPECTRUM, AND THE 
CHEMICAL CONSTITUTION OF THE SUN. THE CHROMO- 
SPHERE AND PROMINENCES. THE CORONA. THE 

SUN'S LIGHT. MEASUREMENT OF THE INTENSITY OF 

THE SUN'S HEAT. THEORY OF ITS MAINTENANCE 

AND SPECULATIONS REGARDING THE AGE OF THE SUN. 

About 1860 the spectroscope appeared in the field as a new 
and powerful instrument for astronomical research, resolving 
at a glance many problems which before seemed to be inacces- 
sible even to investigation. It is not extravagant to say that 
its invention has done almost as much for the advancement of 
astronomy as that of the telescope. 

It enables us to study the light that comes from distant 
objects, to read therein a record, more or less complete, of 
their chemical composition and physical conditions, to measure 
the speed with which they are moving towards or from us ; 
and sometimes, as in the case of the solar prominences, to see, 
and observe at any time, objects otherwise visible only on 
rare occasions. 

193. The Spectroscope. — The essential part of the instru- 
ment is either a prism or train of prisms, or else a diffraction 
" grating," l which is capable of performing the same office of 
" dispersing" the rays of different color. 

If with such a " dispersion piece," as it may be called 

1 The "grating" is merely a piece of glass or speculum metal, ruled 
with many thousand straight, equidistant lines, from 5000 to 20,000 in 
the inch. 



134 THE SPECTROSCOPE. [§ 193 

(either prism or grating), one looks at a distant point of light, 
he will see instead of a point a long streak of light, red at one 
end and violet at the other. If the object looked at is a line 
of light j parallel to the edge of the prism or to the lines of the 
grating, then instead of a mere colored streak without width, 
one gets a "spectrum," — a colored band or ribbon of light, 
which may show markings that will give the observer most 
valuable information (Physics, p. 368). It is usual to form 
this line of light by admitting the light through a narrow 
"slit" placed at one end of a tube, which carries at the other 
end an achromatic object-glass having the slit in its principal 
focus (Physics, p. 359). This tube with slit and lens consti- 
tutes the " collimator "; so named because it is precisely the 
same as an instrument used in connection with the transit 
instrument to adjust its "line of collimation." 

Instead of looking at the spectrum with the naked eye, it 
is better in most cases to use a small "view telescope" (so 
called to distinguish it from the large telescope to which the 
spectroscope is often attached). 

194. Construction of the Spectroscope. — The instrument, 
therefore, as usually constructed, and shown in Fig. 52, con- 
sists of three parts, — collimator, dispersion piece, and view 
telescope, — although in the "direct-vision" spectroscope, 
shown in the figure, the view telescope is omitted. 

Fig. 52, from "The Sun" by permission of Appleton & Co., repre- 
sents a large "tele-spectroscope" as the combination of telescope and 
spectroscope is called, arranged for photographic work. 

If the slit, S, be illuminated by strictly "homogeneous light," 
say yellow, a yellow image of the slit will appear at Y. If, 
at the same time, light of a different wave length, red for in- 
stance, be also admitted, a red image will be formed at R, and 
the observer will then see a spectrum with two bright lines, 
the lines being really nothing more than images of the slit. If 
violet light be admitted, a violet image will be formed at V, 




Fig. 52. — Telespectroscope, fitted for Photography. 



§ 194] CONSTRUCTION OF THE SPECTROSCOPE. 



135 



and there will be three bright lines. If the light comes from 
a luminous solid, like the lime cylinder of a calcium light, or 
the filament of an incandescent lamp, or from an ordinary 
gas or candle flame (Physics, p. 374), there will be an infinite 
number of these slit images close together, without interval 
or break, and we then get what is called a continuous spectrum. 
If it comes, however, from an electric spark or a so-called 
Geissler tube, or from a Bunsen burner flame charged with the 



Prism-Spectroscope 




Grating 



Direct-Vision Spectroscope 
Fig. 52.* — Different Forms of Spectroscope. 

vapor of some volatile metal, the spectrum will consist of a 
series of bright lines, or bands. 

* 194*. The Solar Spectrum. — If we look at sunlight, either 
direct or reflected (as from the moon), we get a spectrum, con- 
tinuous in the main, but crossed by a multitude of dark 
lines, or missing slit-images. These dark lines are known 
as the " Fraunhofer lines," because Fraunhofer was the first 
to map them (in 1814). To some of the more conspicuous 



136 THE SOLAR SPECTRUM. [§ 194* 

ones he assigned letters of the alphabet which are still retained 
as designations : thus A is a strong line at the extreme red 
end of the spectrum ; C, one in the scarlet ; D, in the yellow ; 
F, in the blue ; and If and iT are a pair at its violet extremity. 
Rowland's great photographic map of the spectrum contains 
several thousands, each as permanent a feature of the spectrum 
as rivers and cities are of a geographical chart. Their expla- 
nation remained an unsolved problem for nearly fifty years. 

195. Principles upon which Spectrum Analysis depends. — 
These, substantially as announced by Kirchhoff in 1858, are 
the three following : — 

1st. A continuous spectrum is given by luminous bodies, 
which are so dense that the molecules interfere with each 
other in such a way as to prevent their free, independent, 
luminous vibration ; i.e., by bodies which are either solid or 
liquid, or if gaseous are under high pressure. 

2d. The spectrum of a luminous gas under low pressure is 
discontinuous, and is made up of bright lines or bands : and 
these lines are characteristic; i.e., the same substance under 
similar conditions always gives the same set of lines, and 
generally does so even under conditions differing quite widely ; 
but it may give two or more different spectra when the cir- 
cumstances differ too widely. 

3d. A gaseous substance absorbs from a beam of white 
light passing through it precisely those rays of which its own 
spectrum consists. The spectrum of white light which has 
been transmitted through it then exhibits a "reversed" spec- 
trum of the gas ; i.e., & spectrum which shows dark lines in 
place of the characteristic bright lines. 

This principle of reversal is illustrated by Fig. 53. Suppose 
that in front of the slit of the spectroscope we place a spirit 
lamp with a little carbonate of soda and some salt of thallium 
upon the wick. We shall then get a spectrum showing the 
two yellow lines of sodium and the green line of thallium, all 
bright. If now the lime light be started behind the flame, we 



195] 



PRINCIPLES OF SPECTRUM ANALYSIS. 



13T 



shall at once have the effect shown in the lower figure, — a con- 
tinuous spectrum crossed by black * lines which exactly replace 
the bright lines. Insert a screen between the lamp flame and 
the lime, and the dark lines instantly turn bright again. The 
explanation of the Fraunhofer lines, therefore, is that they are 
mainly due to the action of the gases and vapors of the solar 
atmosphere upon the light that comes from the liauid or solid 
particles composing the photo spheric clouds. Some of them, how- 



Lime 




Fig. 53. — Reversal of the Spectrum. 

ever, known as " Telluric lines" are due to the gases and vapors of 

the earth's atmosphere, — to water- vapor and oxygen especially. 

196. Chemical Constituents of the Sun. — Numerous lines 

of the solar spectrum can be identified as due to the pres- 



1 Their darkening, however, when the light from the lime is trans- 
mitted through the flame, is only relative and apparent, not real. Their 
brightness is actually a little increased ; but that of the background is in- 
creased immensely, making it so much brighter than the lines that, con- 
trasted with it, they look black. 



138 



CHEMICAL CONSTITUENTS OF THE SUN. 



[§ 196 




ence in the sun's atmosphere of known terrestrial elements 
in the state of vapor. To effect the comparison necessary for 
this purpose, the spectroscope must be so arranged that the 

observer can confront the 
spectrum of sunlight with 
that of the substance to be 
tested. In order to do this, 
half of the slit is covered by 
a little " comparison prism " 
(Fig. 54), which reflects into 
it the light from the sun, 
while the other half of the 
slit receives directly the light of some flame or electric spark. 
On looking into the eye-piece of the spectroscope, the observer 
will then see a spectrum, the lower half of which, for instance, 
is made by sunlight, while the upper half is made by light coming 
from an electric arc containing the vapor, say of iron. 

In such comparisons photography may be most effectively used 
instead of the eye. Fig. 55 is a rather unsatisfactory reproduction, on 
a reduced scale, of a negative made in investigating the presence of iron 
in the sun. The lower half is the violet portion of the sun's spectrum 



Fig. 54. — The Comparison Prism. 





Fig. 55. — Comparison of the Spectrum of Iron with the Solar Spectrum. From a 
Negative by Professor Trowbridge. 

and the upper half that of an electric arc charged with the vapor of 
iron. In the original every line of the iron spectrum coincides exactly 
with its correlative in the solar spectrum, though in the engraving 
many of the coincidences fail to be obvious. There are of course, on 
the other hand, certain lines in the solar spectrum which do not find 
any correlative in that of iron, being due to other elements. 



I W7] 



ELEMENTS KNOWN TO EXIST IN THE SUN. 



139 



197, Elements known to exist in the Sun. — As the result 
of such comparisons, first made by Kirchhoff, but since repeated 
and greatly extended by late investigators, a large number 
of the chemical elements have been ascertained to exist in the 
solar atmosphere in the form of vapor. 

Professor Rowland in 1890 gave the following preliminary 
list of thirty-six whose presence he regarded as certainly 
established, and it is probable that the completion of his 
research will add a number of others. 1 The elements are 
arranged in the list according to the intensity of the dark lines 
by which they are represented in the solar spectrum : the 
appended figures denote the rank which each element would 
hold if the arrangement had been based on the number instead 
of the intensity of the lines. In the case of iron the number 
exceeds 2000. 



* Calcium, n. 
*Iron, i. 

* Hydrogen, 22. 

* Sodium. 20. 

* Nickel, 2. 

* Magnesium, 19. 

* Cobalt, 6. 
Silicon, 21. 
Aluminium, 25. 

* Titanium. 3. 

* Chromium, 5. 

* Manganese, 4. 



* Strontium, 23. 
Vanadium, 8. 

* Barium, 24. 
Carbon, 7. 
Scandium, 12. 
Yttrium, 15. 
Zirconium, 9. 
Molybdenum, 17. 
Lanthanum, 14. 
Niobium, 16. 
Palladium, 18. 
Neodymium, 13. 



Copper, 30. 
Zinc, 29. 
Cadmium, 26. 
* Cerium, 10. 
Grlucinum, ^3- 
Germanium, 32. 
Rhodium, 27. 
Silver, 31. 
Tin, 34. 
Lead, 35. 
Erbium, 28. 
Potassium, 36. 



An asterisk denotes that the lines of the element indicated appear 
often or always as bright lines in the spectrum of the chromo- 
sphere. 



It will be noticed that all the bodies named in the list, car- 
bon alone excepted, are metals (chemically hydrogen is a 
1 Helium (see Art. 202*) was added in 1895. • 



140 THE REVERSING LAYER. [§ 19' 



metal), and that many of the most important terrestrial ele- 
ments fail to appear; oxygen, nitrogen, chlorine, bromine, 
iodine, sulphur, phosphorus, and boron are all missing. 

We must be cautious, however, in drawing negative conclusions. It 
is quite conceivable that the spectra of these bodies under solar con- 
ditions may be so different from their spectra as presented in our 
laboratories that we cannot recognize them ; for it is now unquestion- 
able that many substances under different conditions give two or 
more widely different spectra, — nitrogen, for instance. 

Mr. Lockyer thinks it more probable that the missing substances are 
not truly " elementary," but are decomposed or " dissociated " by the 
intense heat, and so cannot exist on the sun, but are replaced by their 
components. He maintains, in fact, that none of our so-called " ele- 
ments " are really elementary, but that all are decomposable, and* are 
to some extent actually decomposed in the sun and stars, and some of 
them by the electric spark in our own laboratories. Granting this, 
many interesting and remarkable spectroscopic facts find easy expla- 
nation. At the same time the hypothesis is encumbered with serrous 
difficulties, and has not yet been finally accepted by physicists and 
chemists. 

198. The Reversing Layer. — According to KirchhofFs theory 
the dark lines are formed by the passing of light emitted by 
the minute solid or liquid particles of which the photospheric 
clouds are supposed to be formed, through somewhat cooler 
vapors containing the substances which we recognize in the 
solar spectrum. If this be so, the spectrum of the gaseous 
envelope, which by its absorption forms the dark lines, should 
by itself show a spectrum of corresponding bright lines. 

The opportunities are rare when it is possible to obtain the 
spectrum of this gas stratum separate from that of the photo- 
sphere ; but at the time of a total eclipse, at the moment when 
the sun's disc has just been obscured by the moon, and the 
sun's atmosphere is still visible beyond the moon's limb, the 
observer ought to see this bright-line spectrum, if the slit of 
' the spectroscope be carefully directed to the proper point, 



: 



§ 198 J THE REVERSING LAYER, 141 

The author succeeded in making this very observation at the Span- 
ish eclipse of 1870. 

The lines of the solar spectrum, which up to the time of the final 
obscuration of the sun had remained dark as usual (with the excep- 
tion of a few belonging to the spectrum of the chromosphere) were 
suddenly "reversed," and the whole length of the spectrum was filled 
with brilliant colored lines, which flashed out quickly and then gradu- 
ally faded away, disappearing in about two seconds, — a most beauti- 
ful thing to see. 

The natural interpretation of this phenomenon is that the forma- 
tion of the dark lines in the solar spectrum is, mainly at least, pro- 
duced by a very thin stratum close down upon the photosphere, since the 
moon's motion in two seconds would cover a thickness of only about 
500 miles. It was not possible, however, to be certain that all the dark 
lines of the solar spectrum were reversed, and in this uncertainty lies 
the possibility of a different interpretation. 

Several partial confirmations have been obtained by various eclipse 
observers since 1870, but at the eclipse of August, 1896, Mr. Shackle- 
ton succeeded in photographing the phenomenon with a so-called 
"prismatic camera," or "objective prism spectroscope" (Arts. 458-9). 
He caught the critical moment exactly, with an exposure of only, half 
a second, and his negative is apparently conclusive in favor of the 
inference stated above. A photograph taken only five seconds later 
shows merely some 20 bright lines belonging to the spectrum of the 
chromosphere (Art. 201), in place of the hundreds shown upon the 
earlier one. 

Mr. Lockyer, however, still continues to dispute the existence of 
any such thin stratum, or "reversing layer." According to his view, 
the solar atmosphere is very extensive, and those lines of the iron 
spectrum, which, as he holds, correspond to the more complex 
combinations of its constituents, are formed only in the regions of 
lower temperature, high up in the sun's atmosphere. 

199. Sun-Spot Spectrum. — The spectrum of a sun spot 
differs from the general solar spectrum not only in its dimin- 
ished brilliancy, but in the great widening of certain lines, 
and the thinning and even "reversing" of others, especially 
those of hydrogen. The majority of the Fraunhofer lines, 
however, are not sensibly affected either way, a fact which Mr. 
Lockyer quotes as evidence that they originate high up in the 



142 



DOPPLEK S PRINCIPLE. 



199 



solar atmosphere rather than in the region of the reversing 
layer close to the photosphere. 

The general darkness of the spot spectrum appears to be due to the 
presence of myriads of extremely fine dark lines, so closely packed as 
to be resolvable only by spectroscopes of great power. This indicates 
that the darkness is caused by the absorption of light by transmission 
through vapors, and is not simply due to the diminished brightness of 
the surface from which the light is emitted. 

200. Distortion of Lines; Doppler's Principle. — Sometimes 
certain lines of the spectrum are bent and broken, as shown in 
Fig. 56. These distortions are explained by the swift motion 
towards or from the observer of the gaseous matter, which by 

its absorption produces the 
line in question. In the 
case illustrated, hydrogen 
was the substance, and its 
motion was toivards the ob- 
server, at one point at the 
rate of nearly 300 miles a 
second. 



\y 



2h 43m 



2h 46m 



2h 51m 



Fm. 56. - 



-The C line in the Spectrum of a Sun 
Spot, Sept. 22, 1870. 

The principle upon which 
the explanation of this displacement and distortion of lines depends 
was first enunciated by Doppler in 1842. It is this : When the dis- 
tance between us and a body which is emitting regular vibrations 
(either of sound or of light) is decreasing, then the number of vibra- 
tions received by us in each second is increased, and their wave-length, 
real or virtual, is correspondingly diminished. 

Thus the pitch of a musical tone rises in the case supposed, and in 
the same way the refrangibility of a light wave, which depends upon 
its wave-length (Physics, p. 383) is increased, so that it will fall 
nearer the violet end of the spectrum (see Appendix, Art. 500). 

201. The Chromosphere. — Outside the photosphere lies the 4 
chromosphere, of which the lower atmosphere, or " reversing lay- 
er/' is only the densest and hottest portion. This chromosphere, 



§201] THE CHROMOSPHERE. 143 

or "color sphere/' is so called because it is brilliantly scarlet, 
owing the color to hydrogen, which is its main, or at least its 
most conspicuous, constituent. In structure it is like a sheet 
of flame overlying the surface of the photosphere to a depth 
of from 5000 to 10,000 miles, and as seen through the tele- 
scope at a total eclipse has been aptly described as like " a 
prairie on fire." 

There is, however, no real "burning" in the case; i.e., no chemical 
combination going on between the hydrogen and some other element like 
oxygen. The hydrogen is too hot to burn in this sense, the tempera- 
ture of the solar surface being above that of " dissociation " ; so high 
that any compound containing hydrogen would there be decomposed. 

202. The Prominences. — At a solar eclipse, after the sun is 
fairly hidden by the moon, a number of scarlet, star-like ob- 
jects are usually seen blazing like rubies upon the contour of 
the moon's disc. In the telescope they look like fiery clouds 
of varying form and size, and as we now know, they are only 
projections from the chromosphere, or isolated clouds of the 
same material. They were called Prominences and Protuber- 
ances, as a sort of non-committal name, while it was still uncer- 
tain whether they were appendages of the sun or of the moon. 

They were first proved to be solar during the eclipse of 1860, 
by means of photographs which showed that the moon's disc 
moved over them as it passed across the sun. Their real 
nature as clouds of incandescent gas was first revealed by the 
spectroscope in 1868, during the Indian eclipse of that year. 
On that occasion numerous observers recognized in their spec- 
trum the bright lines of hydrogen along with another conspic- 
uous yellow line, at first wrongly attributed to sodium, but 
afterwards, to a hypothetical element unknown in our labora- 
tories and provisionally named " Helium," its yellow line be- 
ing known as D z (D x and D 2 being the sodium lines). 

202*. Helium was discovered as a terrestrial element (or perhaps 
a mixture of two or more elements) in April, 1895, by Dr. Ramsay, 
of London, one of the discoverers of Argon. In examining the spec- 



144 - HELIUM. [§ 202* 

brum of the gas extracted from a specimen of Cleveite, a species of 
pitch-blende, he fonnd the characteristic D 3 line along with certain 
other unidentified lines which appear in the spectrum of the chromo- 
sphere and prominences. The same gas has since been found in a 
number of other minerals and in meteoric iron. Its density turns out 
to be about double that of hydrogen, but less than that of any 
other known element. Chemically, it is extremely inert, refus- 





es uiescent Prominences. 




Flames. Jets and Spikes near Sun's Limb, Oct. 5, 1871. 

Eruptive Prominences. 
Fig. o7. 

ing to enter into combination with other elements (as hydrogen 
does so freely), and therefore exists on the earth only in minute 
quantities. It seems, however, to be abundant in certain stars 
and nebulae, where its lines are conspicuous along with those of 
hydrogen. The D 3 line is not the only helium line, but the chromo- 



§ 202*] THE PROMINENCES. 145 

sphere spectrum contains at least three others that are always observ- 
able, besides several that occasionally make their appearance. The 
H and K lines of calcium are also, like those of hydrogen and helium, 
always present as bright lines in the chromosphere ; and several hun- 
dred lines of the spectra of iron, strontium, magnesium, sodium, &c, 
have been observed in it now and then. 

203. The Prominences and Chromosphere observable with 
the Spectroscope. — Janssen was so struck with the brightness 
of the hydrogen lines that he believed it possible to observe 
them in full daylight, and the next day he found it to be so ; 
and not only this, but he found also that by proper manage- 
ment of his spectroscope he could study the forms and struc- 
ture of the prominences nearly as well as during the eclipse. 
Lockyer in England, a few days later, and quite independ- 
ently, made the same discovery, and his name is always 
justly associated with Janssen's. See Appendix, Art. 501. 

It is now possible even to photograph the prominences by 
means of the spectroscope, utilizing the H and K lines of cal- 
cium. Professor Hale, now of the Yerkes Observatory, and 
Deslandres of Paris, have also contrived " spectroheliographs," 
with which they photograph the chromosphere and prominences 
around the whole circumference of the sun by a single exposure. 

204. Different Kinds of Prominences. — The prominences 
may be broadly divided into two classes, — the " quiescent " 
or " diffuse," and the " eruptive," or as Secchi calls them, " the 
metallic" because they show in their spectrum the lines of 
many of the metals in addition to the lines of hydrogen. 

The prominences of the former class, illustrated by the two 
upper figures of Fig. 57, are immense clouds, often 50,000 or 
60,000 miles in height and of corresponding horizontal dimen- 
sions, either resting directly upon the chromosphere as a base, 
or connected with it by stems and columns, though in some 
cases they- appear to be entirely detached from it. They are 
not very brilliant, and ordinarily show no lines in their spec- 



146 



THE PROMINENCES. 



[§204 



trum except those of hydrogen and helium ; nor are their 
changes usually rapid, but they continue sensibly unaltered, 
sometimes for days together ; i.e., as long as they remain in 
sight in passing around the limb of the sun. All their forms 
and behavior indicate that, like the clouds in our own atmos- 
phere, they exist and float, not in a vacuum, but in a medium 
which must have a density comparable with their own, though 
for gome reason not visible in the spectroscope. They are 
found on all portions of the sun's disc, not being confined to 
the sun-spot zones. 





Prominences Sept. 7, 1871, 12.30 p.m. (a) 



Same at 1.15 p.m. (&) 



Fig. 58. 



The eruptive prominences, on the other hand, appear only in 
the spot zones, and as a rule in connection with active spots. 
They usually seem to originate not within the spots them- 
selves but in the surrounding region of disturbed faculae. 
Ordinarily they are not so large as the quiescent prominences, 
but at times they become enormous, reaching elevations of 
several hundred thousand miles. They commonly take the 
form of "spikes," "flames," or "jets," and sometimes they 
are bright enough to be visible with the spectroscope on the 
disc of the sun itself, 



§204] THE CORONA. 147 

They are most fascinating objects to watch, on account of 
the rapidity of their changes. Sometimes their actual motion 
can be perceived directly, like that of the minute hand of a 
clock, and this implies a velocity of at least 250 miles a second 
in the moving mass. In such cases the lines of the spectrum 
are also, of course, greatly displaced and distorted. 

Fig. 58 represents a prominence of this sort at two times, separated 
by an interval of three quarters of an hour. The large quiescent promi- 
nence of Fig. (a) was completely blown to pieces by the " explosion," 
as it may be fairly called, which occurred beneath it. Such occur- 
rences, of course, are not every-day affairs, but are by no means very 
uncommon. 

The number of prominences of both kinds visible at one time on 
the circumference of the sun's disc ranges from one or two to twenty- 
five or thirty ; the eruptive prominences being numerous only near the 
times of sun-spot maximum. 

205. The Corona. — The corona is a halo or glory of light 
which surrounds the sun at the time of a total eclipse, and 
lias been known from remote antiquity as one of the most 
beautiful and impressive of all natural phenomena. The por- 
tion of the corona near the sun is dazzlingly bright and of a 
pearly tinge, which contrasts finely with the scarlet promi- 
nences. It is made up of filaments and rays which, roughly 
speaking, diverge radially, but are strangely curved and inter- 
twined. At a little distance from the edge of the sun the 
light becomes more diffuse, and the outer boundary of the 
corona is not very well defined, though certain dark rifts 
extend through it clear to the sun's surface. Often the fila- 
ments are longest in the sun-spot zones, giving the corona a 
roughly quadrangular form. This seems to be specially the 
case in eclipses which occur near the time of a sun-spot maxi- 
mum. In eclipses which occur near the sun-spot minimum, on 
the other hand, the equatorial rays predominate — diffuse and 
rather faint, but of great extent. Near the poles of the sun 
there are often tufts of sharply defined threads of light, 
which curve both ways 4rom the pole. 



148 THE CORONA. [§205 

The corona varies greatly in brightness at different eclipses, 
according to the apparent diameter of the moon at the time. 
The total light of the corona is certainly always at least two 
or three times as great as that of the full moon. 

206. Drawings and Photographs of the Corona. — There is 
very great difficulty in getting accurate representations of this phe- 
nomenon. The two or three minutes during which only it is visi- 
ble at any given eclipse, do not allow time for trustworthy hand- 
work ; at any rate, drawings of the same corona made even by good 
artists, sitting side by side differ very much, sometimes ridiculously. 
Photographs are better, so far as they go, but hitherto they have not 
succeeded in bringing out many details of the phenomenon w r hich are 
easily visible to the eye ; nor do the pictures which show well the 
outer portions of the corona generally bring out the details near the 
sun's limb. The best results are obtained by making a sort of com- 
posite picture after the eclipse, combining in one representation all 
the features which appear with certainty in any of a series of photo- 
graphs made with varying exposures. Fig. 59 is such a picture, en- 
graved from the photographs of the Indian Eclipse of 1871, taken 
from " The Sun/' by permission of Appleton & Co. 

207. Spectrum of the Corona. — The characteristic feature 
of the visual, spectrum is a bright line in the green, generally 
known as the " 1474 " line, because it coincides with a dark 
line which on KirchhofFs map of the solar spectrum, is found 
at that point on his scale. This dark line had been previously 
identified by Angstrom, as due to iron, and the coincidence 
was for a long time puzzling (since the vapor of iron is a very 
improbable substance to be found at such an elevation above 
the photosphere) until it was discovered that the line is really a 
close double, one of its two components being due to iron, while 
the other is due to some unknown gaseous element, which 
has been called " Goronium " after the analogy of Helium. 

Besides this conspicuous green line there are several others in the 
violet (faintly shown in spectroscopic photographs) which are prob- 
ably due to the same substance. The hydrogen and helium lines, 
and // and K of calcium, have also been rfhotographed as bright lines 



§ 2 °7] NATURE OF THE CORONA. 14 ( <* 

in the corona spectrum ; but observations made in 1893 and 1896 
prove that they are caused by reflection (in our atmosphere) of light 
from the chromosphere and prominences, and are not truly coronal. 

208. Nature of the Corona. — The corona is proved to be a 
true solar appendage and not a mere optical phenomenon, nor 




Fig. 59. —Corona of the Indian Eclipse of 1871. 

due to either the atmosphere of the earth or moon, by two 
unquestionable facts : First, its spectrum as described above 
is not the spectrum of reflected sunlight, but of a glowing gas ; 
and second, photographs of the corona made at widely differ- 



150 INTENSITY OF SUNLIGHT. [§ 208 

ent stations on the track of an eclipse show identical details, 1 
and exhibit the motion of the moon across the coronal fila- 
ments. In a sense, then, the corona is a phenomenon of the 
sun's atmosphere, though the solar " atmosphere " is very far 
from bearing to the sun the same relations that are borne 
towards the earth by the air. The corona is not a simple 
spherical envelope of gas comparatively at rest, and held in 
equilibrium by gravity, but other forces than gravity are prev- 
alent in it, and matter that is not gaseous probably abounds. 
The phenomena of the corona are not yet satisfactorily ex- 
plained, and remind us far more of auroral streamers and 
comets' tails than of anything that occurs in the lower regions 
of our terrestrial atmosphere. 

That the corona is composed of matter excessively rarified 
is shown by the fact that in a number of cases comets are 
known to have passed directly through it (as for instance in 
1882) without the slightest perceptible disturbance or retarda- 
tion of their motion. Its density must, therefore, be almost 
inconceivably less than that of the best vacuum we are able to 
make by artificial means. 

THE SUN'S LIGHT AND HEAT. 

209. The Sun's Light. — By photometric methods, which we 
will not stop to explain (see " General Astronomy") it is found 
that the sun gives us about 1575 billions of billions (1575 fol- 
lowed by 24 ciphers) times as much light as a standard candle 1 
would do at that distance. 



1 There are, however, unquestionable changes in the corona in the 
course of the half-hour or so which may elapse between the pictures when 
the stations are as much as 1000 miles apart; but the changes are not of 
such a sort as to affect the argument. 

2 For definition of standard candle, see Physics, p. 327. 



§ 209] INTENSITY OF SUNLIGHT. 151 

The light received from the sun is about 600,000 times that 
of the moon (Art. 162), about 7,000,000000 times that of 
Sirius, the brightest of the fixed, stars, about 50,000,000000 
times that of Vega or Arcturus, and fully 200,000,000000 times 
that of the Pole-star. 

The " intensity " of sunlight, or the " intrinsic brightness " 
of the sun's surface, is quite a different matter from the total 
quantity of its light expressed in candle power. By intensity 
we mean the amount of light per square unit of luminous surface. 
From the best data we can get (only roughish approximations 
being possible) we find that the sun's surface is about 190,000 
times as bright as that of a candle flame ; and about 150 times 
as bright as the lime of a calcium light ; even the darkest part 
of a sun spot outshines the lime light. 

The brightest part of an electric arc comes nearer sunlight 
in intensity than anything else we know of, being from one- 
half to one-quarter as bright as the solar surface itself. 

210. Comparative Brightness of Different Portions of the 
Sun's Disc. — The sun's disc is brightest near the centre, but the 
variation is slight until we get pretty near the edge ; there the light 
falls off rapidly, so that just at the sun's limb the intensity is not 
much more than one-third as great as at the centre. The color is mod- 
ified also, becoming a sort of orange red, the blue and violet rays 
having lost much more of their brightness than the red and yellow. 

This darkening is unquestionably due to the general absorption of 
light by the lower parts of the sun's atmosphere. Just how much 
the sun's brightness is diminished for us by this absorption, it is dim- 
cult to say. According to Langley, if the sun's atmosphere were sud- 
denly removed, the surface would shine out somewhere from two to 
five times as brightly, and its tint would become strongly blue like the 
color of an electric arc. 

211. The Quantity of Solar Heat: The Solar Constant. — 

The Solar Constant is the number of heat units which a square 
unit of the earth 1 s surface, unprotected by any atmosphere, and 



152 QUANTITY OF SOLAR HEAT. [§ 211 

exposed perpendicularly to the sun's rays would receive from the 
sun in a unit of time. The heat unit most used at present is 
the " Calory" l which is the quantity of heat required to raise 
the temperature of one kilogram of water 1° C. ; and as the 
result of the best observations thus far made, it appears that 
the solar constant is between 25 and 30 of these "calories" 
to a square metre in a minute, under a vertical sun, and after 
allowing for the absorption of a large percentage of heat by 
the air. At the earth's surface a square metre would seldom 
actually receive more than from 10 to 15 calories in a minute. 

212. Method of Determining the Solar Constant. — The 

principle is simple, though the practical difficulties are seri- 
ous, and so far have made it impossible to obtain the accuracy 
desirable. The determination is mad^ by allowing a beam of 
sunlight of "known cross section to fall upon a. known quantity of 
water for a known time and measuring the rise of temperature. 

The difficulty lies partly in measuring and allowing for the heat 
received by the water from other sources than the sun, and for its 
own loss of heat by radiation ; but especially and mainly in deter- 
mining the proper allowance to be made for the absorption of the 
sun's heat in passing through the air. This atmospheric absorption 
changes continually with every change in the transparency of the air 
or of the sun's altitude. (For a description of the Pyrheliometer, see 
Appendix, Art, 556.) 

1 Many writers use a unit of heat a thousand times smaller, i.e., the 
quantity of heat which raises the temperature of one gram of water 1° C. ; 
and they give as the " solar constant " the number of these units received 
per square centimeter in a minute. Since there are 10,000 square centi- 
meters in a square meter, this makes the number expressing the solar 
constant a number just one-tenth as large as that stated above. Thus 
Langley puts it at three " small calories." 

There would be some advantage in expressing this " constant " on the 
"c. g. s. system," (Physics, p. 4). To do this, we should have to divide 
the "number" last given by 60 to reduce the minutes to seconds, so that, 
according to Langley, we should have the solar constant (c. g. s.) 0.050 
44 small calories" per square centimeter per second. 



§ 215] SOLAR HEAT AS ENERGY. 153 

213. The Solar Heat at the Earth's Surface expressed in 
Terms of Melting Ice. — Since it requires 79^ calories of heat 
to melt a kilogram of ice with a specific gravity of 0.92, it 
follows that taking the solar constant at 30, the heat received 
from a vertical sun would melt in an hour a sheet of ice 24.7 
millimeters, or very nearly an inch in thickness. From this, 
it is easily computed that the amount of heat received by the 
earth from the sun in a year is sufficient to melt a shell of ice 
177.4 feet thick all over the earth's surface. 

214. Solar Heat expressed as Energy. — Since according to 
the known value of the " mechanical equivalent of heat " 
(Physics, p. 175) a horse-power (33,000 foot pounds per 
minute) can easily be shown to be equivalent to about 10.7 
calories per minute, it follows that each square meter of the 
earth's surface perpendicular to the sun's rays ought to re- 
ceive about 2.8 horse-power continuously. Atmospheric ab- 
sorption cuts this down to about If horse-power, of which 
about -J can be realized by a suitable machine, such as Erics- 
son's solar engine. 

The energy annually received from the sun by the whole of the 
earth's surface aggregates nearly 100 mile-tons to each square foot. 
That is, the average amount of heat annually received by each square 
foot of the earth's surface, if utilized in a theoretically perfect heat 
engine, would hoist nearly 100 tons to the height of a mile. 

215. Solar Radiation at the Sun's Surface. — If now we 

estimate the amount of radiation at the sun's surface itself, we 
come to results which are simply amazing. We must multiply 
the solar constant observed* at the earth by the square of the 
ratio between 93,000,000 miles (the earth's distance from the 
sun) and 433,250 (the radius of the sun). This square is about 
46,000. In other words, the amount of heat emitted in a 
minute by a square meter of the sun's surface, is about 46,000 
times as great as that received by a square meter at the earth. 
Carrying out the figures, we find that this heat radiation at the 
sun's surface amounts to 1400,000000 calories per square meter 



154 TEMPERATURE OF THE SUN. [§ 216 

per minute; that if the sun were frozen over completely, to a 
depth of 64 feet, the heat emitted would melt the shell in one 
minute; that if a bridge of ice could be formed from the earth 
to the sun by a column of ice 2\ miles square and 93,000,000 
long, and if in some way the entire solar radiation could be 
concentrated upon it, it would be melted in one second, and in 
seven more would be dissipated in vapor. 

Expressing it as energy, we find that the solar radiation is 
over 100,000 horse-power continuously for each square meter of 
the sun's surface. 

These figures are based, of course, on the assumption that the sun 
radiates heat in all directions alike, and there is no reason known to 
science why it should not. 

So far as we can see, only a minute fraction of the whole radiation 
ever reaches a resting place. The earth intercepts about % 2 oWo ooo> 
and the other planets of the solar system receive in all perhaps from 
ten to twenty times as much. Something like tooo^oooo seems to be 
utilized within the limits of the solar system. As for the rest, science 
cannot yet give any certain account of it. 

216. The Sun's Temperature. — As to the temperature of 
the sun's surface, we have no sure knowledge, except that it 
must be higher than that of any artificial heat. While we 
can measure with some accuracy the quantity of heat which 
the sun sends us, our laboratory experiments do not yet fur- 
nish the necessary data from which we can determine with 
certainty what must be the temperature of the sun's surface 
in order to enable it to send out heat at the observed rate. 

The estimates of the temperature of the photosphere run all the 
, \yay from the very low ones of some of the French physicists (who set 
it about 2500° C. — higher, but not vastly higher than that of an electric 
arc) to those of Secchi and Ericsson, who put the figure among the 
millions. The prevailing opinion sets it between 5,000° and 10,000° C. ; 
i.e., from 9,000° to 20,000° F. 




§ 218] INTENSITY OF SOLAK HEAT. 155 

217. The Burning Lens. — A most impressive demonstra- 
tion of the intensity of the sun's heat lies in the fact that in 
the focus of a powerful burning lens all known substances 
melt and vaporize. Now at the focus of a lens the temperature 
can never more than equal that of the source from which the heat 
comes. Theoretically, the limit of temperature is that which 
would be produced by the sun's direct radiation at a distance 
such that the sun's apparent diameter would just equal that 
of the lens viewed from its focus. 

The temperature 
produced at F, Fig. 
60, would, if there 
were no losses, be 
just the same as that 
of a body placed so 
near the sun that the 
sun's angular diame- 
ter equals LFL'. Now, in the case of the most powerful lenses thus 
far made, a body at the focus was thus virtually carried to within about 
240,000 miles from the sun's surface (about the same distance as that 
of the moon from the earth), and here, as has been said, the most 
refractory substances succumb immediately. 

218. Constancy of the Sun's Heat. — It is an interesting 
question, as yet unanswered, whether the total amount of the 
sun's radiation does or does not perceptibly vary. There may 
be considerable fluctuations in the quantity of heat hourly 
received from the sun without our being able to detect them 
surely with our present means of observation. 

As to any steady, progressive increase or decrease of solar 
heat, it is quite certain that no considerable change of that 
kind has been going on for the past 2000 years, because the 
distribution of plants and animals on the earth's surface is 
practically the same as in the days of Pliny ; it is, however, 
rather probable than otherwise that the general climatic 
changes which Geology indicates as having formerly taken 



156 MAINTENANCE OF SOLAR HEAT. [§ 2l9 

place on the earth, — the glacial and carboniferous epochs, for 
instance, — may ultimately be traced to changes in the sun's 
condition. 

219. Maintenance of Solar Heat. — One of the most inter- 
esting and important problems of modern science relates to 
the explanation of the method by which the sun's heat is 
maintained. We cannot here discuss the subject fully, but 
must content ourselves with saying first, negatively, that the 
phenomenon cannot be accounted for on the supposition that 
the sun is a hot, solid or liquid body simply cooling ; nor by 
combustion, nor (adequately) by the fall of meteoric matter on 
the sun's surface, though this cause undoubtedly operates to a 
limited extent : second, positively, the solar radiation can be 
accounted for on the hypothesis first proposed by Helmholtz, 
that the sun is shrinking slowly but continuously. It is a matter 
of demonstration that an annual shrinkage of about 300 feet 
in the sun's diameter would liberate heat sufficient to keep up 
its radiation without any fall in its temperature. If the 
shrinkage were more than 300 feet, the sun would be hotter 
at the end of a year than it was at the beginning. 

It is not possible to exhibit this hypothetical shrinkage as a fact 
of observation, since this diminution of the sun's diameter would 
amount only to a mile in 17.6 years, and nearly 8000 years would be 
spent in reducing it by a single second of arc. No change much 
sinaller than 1" could be certainly detected even by our most modern 
instruments. 

We can only say that while no other theory yet proposed meets the 
conditions of the problem, this appears to do so perfectly, and there- 
fore has high probability in its favor. 

220. Age and Duration of the Sun. — If Helmholtz's theory 
is correct, it follows that in time the sun's heat must come to 
an end, and, looking backward, that it must have had a begin- 
ning. We have not the data for an accurate calculation of the 
sun's future duration, but if it keeps up its present rate of 



I 



§ 221] CONSTITUTION OF THE SUN. 157 

radiation it must, on this hypothesis, shrink to about half its 
diameter in some 5,000,000 years at longest. Since its mean 
density will then be eight times as great as now, it can hardly 
continue to be mainly gaseous (as it probably is at present), 
and its temperature must begin to fall quite sensibly. It is 
not, therefore, likely that the sun will continue to give heat 
enough to support such life on the earth as we are now famil- 
iar with, for much more than 10,000,000 years, if it does it so 
long. 

As to the past, we can be a little more definite. No conclu- 
sion of Geometry is more certain than this, — that the shrink- 
age of the sun to its present dimensions from a diameter 
larger than that of the orbit of Neptune, the remotest of the 
planets, would generate about 18,000,000 times as much heat 
as the sun noiv radiates in a year. Hence, if the sun's 
heat has been and still is ivholly due to the contraction of 
its mass, it cannot have been radiating heat at the present 
rate, on the shrinkage hypothesis, for more than 18,000,000 
years ; and on that hypothesis the solar system in anything 
like its present condition cannot be much more than as old as 
that. 

But notice the " if." It is quite conceivable that the solar system 
may have received in the past other supplies of heat than that due to 
contraction. If so, it may be much older. 

221. Constitution of the Sun. — The received opinion as to 
the constitution of the sun is substantially as follows : — 

(a) As to the condition of the central mass or nucleus of 
the sun, we cannot be said to have definite knowledge. It 
is probably gaseous, this being indicated by the sun's low 
mean density and high temperature ; but at the same time 
this gaseous matter must be in a very different condition from 
gases as we know them in our laboratories, on account of the 
intense heat and the enormous pressure due to the force of 
solar gravity. The central mass, while still possessing the 
characteristic properties of gas (that is, characteristic from 



158 CONSTITUTION OF THE SUN. [§228 

bhe scientific point, of view), must be denser than water, and 
viscous, with a consistency something like pitch or tar. 

While this doctrine as to (he gaseous nature <>l the solar nucleus i| 
generally assented to, there are, however, some authorities who still 
maintain that it is liquid. 

222. (/>) The Photosphere is in all probability a sheet of lumi- 
nous clouds, constituted mechanically like terrestrial clouds, 
i.e., o\' minute solid or liquid particles floating in gas, 

r l 'he photospheric clouds of the sun are supposed to be formed (just 
as snow and rain clouds are in our own atmosphere) by the cooling 

and condensation {A' vapors, and they float in the permanent gases of 
the solar atmosphere in the same way that oui- own clouds do in our 
own atmosphere. We do not know just what materials constitute 
these solar clouds, hut naturally suppose them to he those indicated 

by the Fraunhofer lines, i.e., chiefly the metals, with carbon and its 

chemical conveners. 

223. (c) The Reversing Layer. — The photospheric clouds 
float in an atmosphere containing a considerable quantity of 
the same vapors out of which they themselves have been 
formed, JUSt as in our own atmosphere the air immediately 
surrounding a cloud is saturated with vapor of water. This 
vapor-laden atmosphere, probably comparatively shallow, con- 
stitutes the reversing layer, and by its selective absorption 

produces the dark lines of the solar spectrum, while by its 

general absorption it produces the peculiar darkening at the 

limb of the sun. 

It. will he remembered that Mr. Lockyer and others have been 
disposed to question the existence o( any such shallow absorbing 
stratum, considering that the absorption takes place in all regions of 

the solar atmosphere dp. to a great elevation, but that the photographs 

made at the eclipse o( 1896 (Art. L98) seem to establish its reality. 

224. {(I) The Chromosphere and Prominences are composed 
of permanent gases, mainly hydrogen y helhim^TiA calcium^ which 



§224] 



THE CORONA. 159 



are mingled with the vapors of the reversing stratum in the 
region of the photosphere, but rise to far greater elevatiofrs 
than do the vapors. The appearances are for the most part 
as if the chromosphere were formed of jets of heated gases, 
ascending through the interspaces between the photospheric 
clouds, like flames playing over a coal fire. 

225. (e) The Corona also rests on the photosphere, and the 
characteristic green line of its spectrum (Art. 207) is brightest 
just at the surface of the photosphere in the reversing stratum 
and in the chromosphere itself; but the corona extends to afar 
greater elevation than even the prominences ever reach, and it 
seems to be not entirely gaseous, but to contain, in addition 
the mysterious "coronium," dust and fog of some sort, per- 
haps meteoric. Many of the phenomena of the corona are 
still unexplained, and since thus far it has been observed only 
during the brief moments of total solar eclipses, progress in 
its study has been necessarily slow. 

225*. Numerous attempts have been made to discover some 
method of observing the corona at other times than during an 
eclipse, but thus far without success. The " 1 174" line is not bright 
enough to render feasible the spectroscopic method, which succeeds 
with the prominences ; and if it were, the fact that the streamers of 
the corona are probably in the main, not gaseous, but of dust-like 
constitution (giving therefore only the spectrum of reflected sunlight), 
would make the spectroscofnc image, even if it could be obtained, 
extremely incomplete : the streamers would not appear in it at all. 

Dr. Iluggins, and others under his direction or following his sug- 
gestion, worked very hard for several years, beginning with 188o, 
in the endeavor to photograph the corona without an eclipse. Some 
of the plates showed, around the image of tfre sun, halo-forms which 
certainly looked very coronal. But it was soon found that plat<\s 
exposed in rapid succession did not agree as to details, and there can 
be no doubt that the apparent "coronas" were not images of the 
real one. The illumination of our own atmosphere near the disc of 
the sun is far too brilliant to allow us, working through it, either to 
see, or to photograph, the much fainter corona behind it. 



160 THE CORONA. [§225* 

Various other methods have been vainly tried, and others have 
been planned and will be executed. The problem is by no means 
even yet given up as absolutely hopeless, though the prospect of 
success is not very promising. 

As has been already said, the real nature of the corona is still 
problematical. In many ways it strongly resembles our terrestrial 
Aurora Borealis and the phenomena which, under certain circum- 
stances, accompany electrical discharges in a partial vacuum. By 
many, therefore, it is regarded as something of the same sort on the 
solar scale of magnitude. Professor Schaberle, of the Lick Obser- 
vatory, on the other hand, urges a purely "mechanical theory" which 
regards the corona as formed by streams or jets of some rare 
material ejected mainly from the sun-spot zones, repelled to planetary 
distances, and then falling back upon the solar surface. Many of 
the peculiar features of the visible corona are then easily explained 
as mere perspective effects due to the apparent superposition and 
interlacing of these ascending and descending streams. 



§ 226J ECLIPSES. 161 



CHAPTER VIII. 

ECLIPSES. — FORM AND DIMENSIONS OF SHADOWS. — 
ECLIPSES OF THE MOON. — SOLAR ECLIPSES. — TOTAL, 
ANNULAR, AND PARTIAL. — ECLIPTIC LIMITS AND 
NUMBER OF ECLIPSES IN A YEAR. — RECURRENCE OF 
ECLIPSES AND THE SAROS. — OCCULTATIONS. 

226. The word " Eclipse " (literally a " faint " or " swoon ") 
is a term applied to the darkening of a heavenly body, espe- 
cially of the sun or moon, though some of the satellites of 
other planets besides the earth are also " eclipsed." An eclipse 
of the moon is caused by its passage through the shadow of 
the earth ; eclipses of the sun, by the interposition of the 
moon between the sun and the observer, or, what comes to the 
same thing, by the passage of the moon's shadow over the 
observer. 

The shadow (Physics, p. 323) is the space from which sun- 
light is excluded by an intervening body : geometrically speak- 
ing it is a solid, not a surface. If we regard the sun and the 
other heavenly bodies as spherical, these shadows are cones 
with their axes in the line joining the centres of the sun 
and the shadow-casting body, the point being always directed 
away from the sun. 

227. Dimensions of the Earth's Shadow. — The length of 
the earth's shadow is easily found. In Fig. 61 we have, from 
the similar triangles OED and ECa, 



162 



THE EARTHS SHADOW. 



[§227 



OD:Ea::OE: EC, or L. 

OD is the difference between the radii of the sun and the 
earth, = R — r. Ea = r, and OE is the distance of the earth 
from the sun = D. Hence 



L = D 



108.5 



D. 



(The fraction 108.5 is found by simply substituting for R and 
r their values.) This gives 857,000 miles for the length of 
the earth's shadow when D has its mean value of 93,000000 
miles. The length varies about 14,000 miles on each side of 
the mean, in consequence of the variation of the earth's dis- 
tance from the sun at different times of the year. 




Fig. 61. — The Earth's Shadow. 

From the cone aCb all sunlight is excluded, or would be were it 
not for the fact that, the atmosphere of the earth by its refraction 
bends some of the rays into this shadow. The effect of this atmos- 
pheric refraction is to increase the diameter of the shadow about two 
per cent, but to make it less perfectly dark. 

228. Penumbra. — If we draw the lines Ba and Ab (Fig. 
61), crossing at P, between the earth and the sun, they will 
bound the "penumbra " within which a part, but not the whole, 
of the sunlight is cut off: an observer outside of the shadow but 
within this cone-frustum, w r hich tapers towards the sun, would 
see the earth as a black body encroaching on the sun's disc. 



§228] ECLIPSES OF THE MOON. 163 

While the boundaries of the shadow and penumbra are perfectly 
definite geometrically, they are not so optically. If a screen were 
placed at M, perpendicular to the axis of the shadow, no sharply 
defined lines would mark the boundaries of either shadow or penum- 
bra. Near the edge of the shadow the penumbra would be very 
nearly as dark as the shadow itself, only a mere speck of the sun 
being there visible ; and at the outer edge of the penumbra the shad- 
ing would be still more gradual. 

229. Eclipses of the Moon. — The axis or central line of the 
earth's shadow is always directed to a point directly opposite 
the sun. If, then, at the time of the full moon, the moon 
happens to be near the ecliptic (i.e., not far from one of the 
nodes of her orbit), she will pass through the shadow and be 
eclipsed. Since, however, the moon's orbit is inclined to the 
ecliptic, lunar eclipses do not happen very frequently, — sel- 
dom more than twice a year. Ordinarily the full moon passes 
north or south of the shadow without touching it. 

Lunar eclipses are of two kinds, — partial and total: total 
when she passes completely into the shadow, partial when she 
only partly enters it, going so far to the north or south of the 
centre of the shadow that only a portion of her disc is obscured. 

230. Size of the Earth's Shadow at the Point where the 
Moon crosses it. — Since EG, in Fig. 61, is 857,000 miles, and 
the distance of the moon from the earth is on the average 
about 239,000 miles, CM must average 618,000 miles, so that 
MN, the semi-diameter of the shadow at this point, will be |4-|- 
the earth's radius. This gives 3jTjV= 2854 miles, and makes 
the whole diameter of the shadow a little over 5700 miles, — 
about two and two-thirds times the diameter of the moon. 
But this quantity varies considerably ; the shadow where it is 
crossed by the moon is sometimes more than three times her 
diameter, sometimes hardly more than tw r ice. 

An eclipse of the moon, when central, i.e., when the moon 
crosses the centre of the shadow, may continue total for about 



164 LUNAR ECLIPTIC LIMIT. [§ 230 

two hours, the interval from the first contact to the last being 
about two hours more. This depends upon the fact that the 
moon's hourly motion is nearly equal to its own diameter. 

The duration of a non-central eclipse varies, of course, 
according to the part of the shadow traversed by the moon. 

231. Lunar Ecliptic Limit. — The lunar ecliptic limit is the 
greatest distance from the node of the moon's orbit at which 
the sun can be at the time of a lunar eclipse. This limit 
depends upon the inclination of the moon's orbit, which is 
somewhat variable, and also upon the distance of the moon 
from the earth at the time of the eclipse, which is still more 
variable. Hence we recognize two limits, the major and 
minor. If the distance of the sun from the node at the time 
of full moon exceeds the major limit, an eclipse is impossible ; 
if it is less than the minor, an eclipse is inevitable. The 
major limit is found to be 12° 15' ; the minor, 9° 30'. Since 
the sun, in its annual motion along the ecliptic, travels 12° 15' 
in less than 13 days, it follows that every eclipse of the moon 
must take place within 13 days from the time when the sun 
crosses the node. 

232. Phenomena of a Total Lunar Eclipse. — Half an hour 
or so before the moon reaches the shadow, its limb begins to 
be sensibly darkened by the penumbra, and the edge of the 
shadow itself when it is first reached appears nearly black by 
contrast with the bright parts of the moon's surface. To the 
naked eye 1^he outline of the shadow looks reasonably sharp; 
but even with a small telescope it is found to be indefinite, 
and with a large telescope and high magnifying power it 
becomes entirely indistinguishable, so that it is impossible to 
determine within half a minute or so the time when the 
boundary of the shadow reaches any particular point on the 
moon. After the moon has wholly entered the shadow, her 
disc is usually distinctly visible, illuminated with a dull, cop- 



§ 232 J COMPUTATION OF A LUNAR ECLIPSE. 165 

per-colored light, which is sunlight, deflected around the earth 
into the shadow by the refraction of our atmosphere, as illus- 
trated by Fig. 62. 

Even when the moon is exactly central in the largest possible 
shadow, an observer on the moon would see the disc of the earth 
surrounded by a narrow ring of brilliant light, colored with sunset 
hues by the same vapors which tinge terrestrial sunsets, but acting 
with double power because the light has traversed a double thickness 
of our air. If the weather happens to be clear at this portion of the 
earth (upon its rim, as seen from the moon), the quantity of light 
transmitted through our atmosphere is very considerable, and the 




Fig. 62. — Light bent into Earth's Shadow by Refraction. 

moon is strongly illuminated. If, on the other hand, the weather hap- 
pens to be stormy in this region of the earth, the clouds cut off nearly 
all the light. In the lunar eclipse of 1884, the moon was absolutely 
invisible for a time to the naked eye, — a very unusual circumstance 
on such an occasion. During the eclipse of Jan. 28th, 1888, although 
the moon was pretty bright to the eye, Pickering found that its pho- 
tographic power, when centrally eclipsed, was only about i-^ioooo °f 
what it was when uneclipsed. 

233. Computation of a Lunar Eclipse. — Since all the phases 
of a lunar eclipse are seen everywhere at the same absolute 
instant wherever the moon is above the horizon, it follows 
that a single computation giving the G-reemvich times of the 
different phenomena is all that is needed. Such computations 
are made and published in the Nautical Almanac. Each 
observer has only to correct the predicted time by simply 
adding or subtracting his longitude from Greenwich, in order 
to get the true local time. The computation of a lunar eclipse 
is not at all complicated, but lies rather beyond the scope of 
this work. 



166 



ECLIPSES OF THE SUN. 



[§234 



ECLIPSES OF THE SUN. 

234. Dimensions of the Moon's Shadow. — By the same 
method as that used for the shadow of the earth (Art. 227) 
we find that the length of the moon's shadow at any time is 
very nearly ¥ ^ of its distance from the sun, and averages 
232,150 miles. It varies not quite 4000 miles each way, rang- 
ing from 236,050 to 228,300 miles. 

Since the mean length of the shadow is less than the mean 
distance of the moon from the earth (238,800 miles), it is evi- 
dent that on the average the shadow will fall short of the 
earth. On account of the eccentricity of the moon's orbit, 
however, she is much of the time considerably nearer than at 
others, and may come within 221,600 miles from the earth's 
centre, or about 217,650 miles from its surface. If at the 

B 




^ > To Sun 

Fig. 63. — The Moon's Shadow on the Earth. 



same time the shadow happens to have its greatest possible 
length, its point may reach nearly 18,400 miles beyond the 
earth's surface. In this case the cross-section of the shadow 
where the earth's surface cuts it (at O in Fig. 63) will be 
about 168 miles in diameter, which is the largest value possible. 
If, however, the shadow strikes the earth's surface obliquely, 
the shadow spot will be oval instead of circular, and the 
extreme length of the oval may much exceed the 168 miles. 

Since the distance of the moon may be as great as 252,970 
miles from the earth's centre, or nearly 249,000 miles from its 
surface, while the shadow may be as short as 228,300 miles, we 
may have the state of things indicated by placing the earth at 
B, in Fig. 63. The vertex of the shadow, V, will then fall 



§ 234] TOTAL AND ANNULAR ECLIPSES. 167 

21,000 miles short of the surface, and the cross-section of the 
" shadow produced " will have a diameter of 196 miles at 0', 
where the earth's surface cuts it. When the shadow falls near 
the edge of the earth, this cross-section may, however, be as 
great as 230 miles. 

235. Total and Annular Eclipses. — To an observer within 
the true shadow cone {i.e., between V and the moon, in Fig. 
63) the sun will be totally eclipsed. An observer in the " pro- 
duced 5 ' cone beyond Twill see the moon smaller than the sun, 
leaving an uneclipsed ring around it, and will have what is 
called an annular eclipse. These annular eclipses are consid- 
erably more frequent than the total, and now and then an 
eclipse is annular in part of its course across the earth and 
total in part. (The point of the moon's shadow extends in 
this case beyond the surface of the earth, but does not reach 
as far as its centre.) 

236. The Penumbra and Partial Eclipses. — The penumbra 
can easily be shown to have a diameter on the line CD (Fig. 
63) of a trifle more than twice the moon's diameter. An 
observer situated within the penumbra has a partial eclipse. 
If he is near the cone of the shadow, the sun will be mostly 
covered by the moon, but if near the outer edge of the penum- 
bra, the moon will only slightly encroach on the sun's disc. 
While, therefore, total and annular eclipses are visible as such 
only by an observer within the narrow path traversed by the 
shadow spot, the same eclipse will be visible as & partial one 
everywhere within 2,000 miles on each side of the path ; and 
the 2,000 miles is to be reckoned perpendicularly to the axis 
of the shadow, and may correspond to a much greater distance 
on the spherical surface of the earth. 

237. Velocity of the Shadow and Duration of Eclipses. — 

Were it not for the earth's rotation, the moon's shadow would 
pass an observer at the rate of nearly 2100 miles an hour. 



168 VELOCITY OF THE SHADOW. [§ 2 *~ 

The earth, however, is rotating towards the east in the same 
general direction as that in which the shadow moves, and at 
the equator its surface moves at the rate of about 1040 miles 
an hour. An observer, therefore, on the earth's equator with 
the moon near the zenith would be passed by the shadow with 
a speed of about 1 060 miles an hour (2100 — 1040), and this is 
the shadow's lowest velocity, — about equal to that of a can- 
non-ball. In higher latitudes, where the surface velocity due 
to the earth's rotation is less, the relative speed of the shadow 
is higher ; and where the shadow falls very obliquely, as it 
does when an eclipse occurs near sunrise or sunset, the advance 
of the shadow on the earth's surface may become very swift, 
as great as 4000 or 5000 miles an hour. 

A total eclipse of the sun observed at a station near the 
equator, under the most favorable conditions possible, may 
continue total for 7 m 68 s , In latitude 40°, the duration can 
barely equal 0>\ m . The greatest possible excess of the radius 
of the moon over that of the sun is only 1' JO". 

At the equator an annular eclipse may last for ll >m l ) 4 s , the 1 
maximum width of the ring of the sun visible around the 
moon being V 37". 

Tn the observation of an eclipse four contacts are recognized: the 
first when the edge of the moon first touches the edge of the sun, 
the second when the eclipse becomes total or annular, the third at the 
cessation of the total or annular phase, and the fourth when the moon 
finally leaves the solar disc. From the first contact to the fourth the 
time may be a little over two hours. 

238. The Solar Ecliptic Limits. — It is necessary, in order to 
have an eclipse of the sun, that the moon should encroach on the cone 
.1 ( 7)7) (Fig. 64), which envelopes the earth and sun. In this case 
the true angular distance between the centres of the sun and moon, 
i.e., their distance as seen from the centre of the earth, would be the 
angle MES. This angle may range from 1° 34' W to 1° 24' 19", 
according to the changing distance of the sun and moon from the 
earth. The corresponding distances of the sun from the node, taking 



§238] 



PHENOMENA OF A SOLAR ECLIPSE. 



169 



into account the variations in the inclination of the moon's orbit, give 
18° 31' and 15° 21' for the major, and minor ecliptic limits. 

In order that an eclipse may be central (total or annular) at any 
part of the earth, it is necessary that the moon should lie wholly 
inside the cone ACBD, as Af, and the corresponding major and minor 
central ecliptic limits come out 11° 50' and 9° 55'. 




Fig. 64. — Solar Ecliptic Limits. 

239. Phenomena of a Solar Eclipse. — There is nothing of 
special interest until the sun is mostly covered, though before 
that time the shadows cast by the foliage begin to be peculiar. 

The light shining through every small interstice among the leaves, 
instead of forming as usual a circle on the ground, makes a little cres- 
cent — an image of the partly covered sun. 



About ten minutes before totality the darkness begins to be 
felt, and the remaining light, coining, as it does, from the edge 
of the sun alone, is much altered in quality, producing an 
effect very like that of a calcium light, rather than sunshine. 
Animals are perplexed and birds go to roost. The tempera- 
ture falls, and sometimes dew appears. In a few moments, if 
the observer is so situated that his view commands the distant 
horizon, the moon's shadow is seen coming, much like a heavy 
thunder-storm, and advancing with almost terrifying swift- 
ness. As soon as the shadow arrives, and sometimes a little 
before, the corona and prominences become visible, while the 
brighter planets and the stars of the first three magnitudes 



170 OBSERVATION OF AN ECLIPSE. [§ 239 

make their appearance. The suddenness with which the dark- 
ness pounces upon the observer is startling. The sun is so 
brilliant that even the small portion which remains visible 
up to within a very few seconds of the total obscuration so 
dazzles the eye that it is unprepared for the sudden transition. 
In a few moments, however, vision adjusts itself, and it is 
then found that the darkness is not really very intense. 

If the totality is of short duration (that is, if the diameter of the 
moon exceeds that of the sun by less than a minute of arc), the corona 
and chromosphere, the lower parts of which are very brilliant, give 
light at least three or four times that of the full moon. Since, more- 
over, in such a case the shadow is of small diameter, a large quantity 
of light is also sent in from the surrounding air, where, 30 or 40 miles 
away, the sun is still shining ; and what may seem remarkable, this 
intrusion of outside light is greatest under a cloudy sky. In such an 
eclipse there is not much difficulty in reading an ordinary watch-face. 
In an eclipse of long duration, say five or six minutes, it is much 
darker, and lanterns become necessary. 

240. Observation of an Eclipse. — A total solar eclipse offers 
opportunities for numerous observations of great importance which 
are possible at no other time, besides certain others which can also be 
made during a partial eclipse. We mention 

(a) Times of the four contacts, and direction of the line joining 
the "cusps" of the partially eclipsed sun. These observations 
determine with extreme accuracy the relative positions of the sun and 
moon at the moment, (b) The search for intra-Mercurial planets, 
(c) Observations of certain peculiar dark fringes which appear upon 
the surface of the earth at the moment of totality, (d) Photometric 
measurement of the intensity of light at different stages of the 
eclipse, (e) Telescopic observations of the details of the prominences 
and of the corona. (/) Spectroscopic observations (both visual and 
photographic) upon the spectra of the lower atmosphere of the 
sun, of the prominences, and of the corona, (g) Observations 
with the polariscope upon the polarization of the light of the 
corona. (Ji) Drawings and photographic pictures of the corona 
and prominences. 



§ 241] CALCULATION OF A SOLAK ECLIPSE. 171 

241. Calculation of a Solar Eclipse. — The calculation of a 
solar eclipse cannot be dealt with in any such summary way 
as that of a lunar eclipse, because the times of contact and 
other phenomena are different at every different station. 
Moreover, since the phenomena of a solar eclipse admit of 
extremely accurate observation, it is necessary to take account 
of numerous little details which are of no importance in lunar 
eclipses. The Nautical Almanacs give, three years in advance, 
a chart of the track of every solar eclipse, and with it data for 
the accurate calculation of the phenomena at any given place. 

Oppolzer, a Viennese astronomer, lately deceased, published a few 
years ago a remarkable book, entitled " The Canon of Eclipses," con- 
taining the elements of all eclipses (8,000 solar and 5,200 lunar) 
occurring between the year 1207 B.C. and 2162 a.d., with maps show- 
ing the approximate track of the moon's shadow on the earth. It in- 
dicates total eclipses visible in the United States in 1900, 1918, 1923, 
1925, 1945, 1979, 1984, and 1994. 

242. Number of Eclipses in a Year. — The least possible 
number is two, both of the sun ; the largest seven, five solar 
and two lunar. The most usual number of eclipses is four. 

The eclipses of a given year always take place at two op- 
posite seasons (which may be called the "eclipse months" of 
the year), near the times when the sun crosses the nodes of 
the moon's orbit. Since the nodes move westward around the 
ecliptic once in about 19 years (Art. 142), the time occupied 
by the sun in passing from a node to the same node again is 
only 346.62 days, which is sometimes called the "eclipse year" 

In an eclipse year there can be but two lunar eclipses, since twice the 
maximum lunar ecliptic limit (2 X 12° 15') is less than the distance the 
sun moves along the ecliptic in a synodic month (29° 6') ; the sun there- 
fore cannot possibly be near enough the node at both of two successive 
full moons ; on the other hand, it is possible for a year to pass without 
any lunar eclipse, the sun being too far from the node at all four of the 
full moons which occur nearest to the time of its node-passage. 



172 FREQUENCY OF ECLIPSES. [§ 242 

In a calendar year (of 365 \ days) it is, however, possible to have 
three lunar eclipses. If one of the moon's nodes is passed by the sun 
in January, it will be reached again in December, the other node hav- 
ing been passed in the latter part of June, and there may be a lunar 
eclipse at or near each of these three node-passages. This actually 
occurred in 1852, and will happen again in 1898 and 1917. 

As to solar eclipses, it is sufficient to say that the solar ecliptic lim- 
its are so much larger than the lunar, that there must be at least one 
solar eclipse at each node-passage of the year, at the new moon next 
before or next after it ; and there may be two, thus making four in 
the eclipse year. (When there are two solar eclipses at the same node, 
there will always be a lunar eclipse at the full moon between them.) 
In the calendar year, a fifth solar eclipse may come in if the first 
eclipse month falls in January. Since a year with five solar eclipses in 
it is sure to have two lunar eclipses in addition, they will make up 
seven in the calendar year. This will happen next in 1935. 

243. Frequency of Solar and Lunar Eclipses. — Taking the 
whole earth into account, the solar eclipses are the more 
numerous, nearly in the ratio of three to two. It is not so, how- 
ever, with those which are visible at a given place. A solar 
eclipse can be seen only from a limited portion of the globe, 
while a lunar eclipse is visible over considerably more than 
half the earth, — either at the beginning or the end, if not 
throughout its whole duration; and this more than reverses 
the proportion between lunar and solar eclipses for any given 
station. 

Solar eclipses that are total somewhere or other on the 
earth's surface are not very rare, averaging one for about every 
year and a half. But at any given place the case is very differ- 
ent : since the track of a solar eclipse is a very narrow path 
over the earth's surface, averaging only 60 or 70 miles in 
width, we find that in the long run a total eclipse happens at 
any given station only once in about 360 years. 

During the 19th century, six shadow tracks have already traversed 
the United States, and one more will do so on May 27th, 1900, the 
path in this case running from Texas to Virginia. 



I 244 1 BECXJREBNCB OF ECLIPSES. 173 

244. Recurrence of Eclipses ; the Saros. — It was known 
to the Chaldeans, even in prehistoric times, that eclipses occur 
at a regular interval of 18 years and 111 days (10i days if 
there happen to be five leap years in the interval). They 
named this period the " Saros." It consists of 223 synodic 
months, containing 6585.32 days, while 19 "eclipse years" 
contain 6585.78. The difference is only about 11 hours, in 
which time the sun moves on the ecliptic about 28 f . If, there- 
fore, a solar eclipse should occur to-day with the sun exactly 
at one of the moon's nodes, at the end of 223 months the new 
moon will find the sun again close to the node (28' west of it), 
and a very similar eclipse will occur again ; but the track of 
this new eclipse will lie about 8 hours of longitude further 
west on the earth, because the 223 months exceed the even 
6585 days by T 3 ^ of a day, or 7 hours, 42 minutes. The usual 
number of eclipses in a Saros is about 71, varying two or three 
one way or the other. 

In the Saros closing Dec. 22d, 1889, the total number was 72,-29 
lunar and 43 solar. Of the latter, 29 were central (13 total, 16 annu- 
lar), and 14 were only partial. The following may be given as an 
example of the recurrence of eclipses at the end of a Saros : The 
four eclipses of 1878 occurred (1) on Feb. 2d, solar, annular; 
(2) Feb. 17th, lunar, partial ; (3) July 29th, solar, total ; (4) Aug. 
12th, lunar, partial. In 1896 the corresponding eclipses were Feb. 
13th, solar, annular ; Feb. 28th, lunar, partial ; Aug. 9th, solar, total ; 
Aug. 23d, lunar, partial. It is usual to speak of the eclipse of Aug. 
9th, 1896, for instance, as a recurrence of the eclipse of July 29, 1878, 
one Saros period earlier. 

245. Occultations of the Stars. — In theory and computation, 
the occultation of a star is identical with an eclipse, except 
that the shadow of the moon cast by the star is sensibly a 
cylinder, instead of a cone, and has no penumbra. Since the 
moon always moves eastward, the star disappears at the moon's 
eastern limb, and reappears on the western. Under all ordi- 
nary circumstances, both disappearance and reappearance are 



1^4 ANOMALOUS PHENOMENA. T§ 246 

instantaneous, indicating not only that the moon has no 
sensible atmosphere, but also that the (angular) diameter of 
even a very bright star is less than 0".02. Observations of 
occultations determine the place of the moon in the sky with 
great accuracy, and when made at a number of widely separ- 
ated stations they furnish a very precise determination of the 
moon's parallax and also of the difference of longitude be- 
tween the stations. 

246. Anomalous Phenomena. — Occasionally, the star, instead 
of disappearing suddenly when struck by the moon's limb (faintly 
visible by "earth-shine"), appears to cling to the limb for a second or 
two before vanishing. In a few instances it has been reported as 
having reappeared and disappeared a second time, as if it had been 
for a moment visible through a rift in the moon's crust. In some 
cases the anomalous phenomena have been explained by the subse- 
quent discovery that the star was double, but many of them still 
remain mysterious, though it is quite likely that they were often 
illusions due to physiological causes in the observer. 



§247] CELESTIAL MECHANICS. 175 



CHAPTER IX. 

CELESTIAL MECHANICS. 

the laws of central force. — circular motion. — 
kepler's laws, and newton's verification of 
the theory of gravitation. — the conic sec- 
tions. — the problem of two bodies. the prob- 
lem of three bodies and perturbations. — the 

TIDES. 

It is, of course, out of the question to attempt in the pres- 
ent work any extended treatment of the theory of the motion 
of the heavenly bodies ; but quite within the reach of those 
for whom this volume is designed there are certain funda- 
mental facts and principles, so important, and in fact, essen- 
tial to an intelligent understanding of the mechanism of the 
solar system, that we cannot pass them in silence. 

247. Motion of a Body Free from the Action of any Force. — 

According to the first law of motion (Physics, p. 65) a moving 
body left to itself describes a straight line with a uniform velocity. 
If we find a body so moving, we may infer, therefore, that it 
is either acted on by no force whatever, or, if forces are acting 
upon it, that they exactly balance each other. 

It is usual with some writers to speak of a body thus moving uni- 
formly in a straight line as actuated by a " projectile force" ; a most 
unfortunate expression, against which we wish to protest vigorously. 
It is a survival of the old Aristotelian idea that rest is more " natu- 
ral " to matter than motion, and that when a body moves, force must 
operate to keep it moving. This is not true. Not motion, but the 
change of motion, either iii speed or in direction, — this alone implies 
the action of " force." 



176 



MOTION UNDER ACTION OF FORCE. 



[§248 




Fig. 65. — Curvature of au Orbit. 



248. Motion under the Action of a Force. — If the motion 
of a body is in a straight line but with varying speed, we infer 
a force acting exactly in the line of motion. If the body moves 
in a curve, we know that some force is acting across the line 
rf . of motion : if the velocity keeps 

increasing, we know that the di- 
rection of the force that acts is 
forward, like a b in Fig. 65, mak- 
ing an angle of less than 90° with 
the " line of motion " * a t ; and 
vice versa, if the motion of the 
body is retarded. If the speed is 
constant, we know that the force must continually act on the 
line a c exactly perpendicular to the line of motion. 

Here, also, we find many writers, the older ones especially, bringing 
in the "projectile force" and saying that when a body moves in a 
curve, it does so " nnder the action of two forces ; one the force that 
draws it sideways, the other the 'projectile force* directed along its 
path." We repeat, this "projectile force" has no present existence nor 
meaning in the problem of a body's motion. Such a force may have put 
the body in motion long ago, but its function has ceased, and now we 
have only to do with the action of one single force, — the deflecting 
force, which alters the direction and velocity of the body's motion. 
From a curved orbit we can only infer the necessary existence of one 
force. We do not mean to say that this force may not be the " result- 
ant " of several ; it often is ; but a single force is all that is necessary 
to produce motion in a curve. 



249. Law of Equal Areas in the Case of a Body moving 
under the Action of a Force directed towards a Fixed Point. 

— In this case it is easy to prove that the path of the body 
will be a curve (not necessarily a circle) , " concave " towards 
the centre of force ; that it will all lie in one plane, and that the 

1 The " line of motion " of a body at any instant is the tangent drawn 
to the curve in which the body travels, at the point occupied by the body. 



§249] 



CIRCULAR MOTION. 



177 



body will move in such a way that its " radius vector " (the 
line that joins the body to the centre of force) will describe 
areas proportional to the time. 

Thus in Fig. 66, the areas aSb, cSd, 
and eSf, are all equal ; the arcs ab, cd, 
and ef, being each described in a unit of 
time, under the action of a " central" 
force, always directed towards S. 

We have already seen that as a 
matter of fact the earth obeys this 
law in moving around the sun (Art. 
118), and the moon in her orbit 
around the earth. Newton showed 
that if the force which keeps them 
in their orbits acts always along the radius vector, they must 
do so of necessity. See Appendix, Art. 502. 




Fig. 66. — The Law of Equal Areas. 



250. Circular Motion. — In the special case when the path of a 
body is a circle described under the action of a force directed to its 
centre, its velocity is constant The force, moreover, is constant, and 
in works upon Mechanics (see Physics, p. 74 ; but in the Physics 
the letter a replaces our /) is easily proved to be given by the formula 



r 



(«) 



In this formula, V is the velocity in feet per second, while r is the 
radius of the circle, and / is the central force measured by the " accel- 
eration" of the body towards the centre, 1 — just as the force of gravity 
is expressed by the quantity g (32 J feet, or 386 inches). 

For many purposes it is desirable to have a formula which shall 
substitute for V (which is not given directly by observation) the time 



1 If we want the central force in pounds, the formula becomes 

V 2 
/lbs. = W X — , W being the weight of the body in pounds. 
gr 



178 kepler's laws. [§ 250 

of revolution, t, which is so given. Since V equals the circumference 

of the circle divided by t, or , we have at once, by substituting 

this value for V in equation («), 

an expression to which we shall frequently refer. 

KEPLER'S LAWS. 

251. Early in the 17th century Kepler discovered, as unex- 
plained facts, three laws which govern the motions of the plan- 
ets, — laws which still bear his name. He worked them out 
from a discussion of the observations which Tycho Brahe had 
made through many preceding years. They are as follows : — 

I. The orbit of each planet is an ellipse with the sun in one 
of its foci. See Art. 117. 

II. The radius vector of each planet describes equal areas in 
equal times. 

III. The squares of the periods of the planets are propor- 
tional to the cubes of their mean distances from the sun; i.e., 
i{ : tr : : af : aj\ This is the so-called " Harmonic law." 

252. To make sure that the student apprehends the meaning and 
scope of this third law, we append a few simple examples of its appli- 
cation. 

1. What would be the period of a planet having a mean distance 
from the sun of one hundred astronomical units; i.e., a distance a 
hundred times that of the earth? 

is : 100 8 = l 2 (year) :Z 2 ; 

whence, X (in years) = VlOO 3 - 1000 years. 

2. What would be the distance from the sun of a planet having a 
period of 125 years? 

l 2 (year) : 125 2 = l 8 : .Y 3 ; whence X= </V2&= 25 astron. units. 



§252] INFERENCES FROM KEPLER'S LAWS. 179 

3. What would be the period of a satellite revolving close to the 
earth's surface V 

(Moon's Dist.) 3 : (Dirt, of Satellite) 3 = (27.3 days) 2 : X'\ 
or, GO 3 : l 3 = 27.3 2 : X 2 ; 

whence, JC= 27 - 8 jyB = P 24". 

V60 3 

253. Many surmises were early made as to the physical 
meaning of these laws. More than one person guessed that a 
force directed towards the sun might be the explanation. 
Newton proved it. He demonstrated the law of equal areas 
and its converse as necessary consequences of the laws of 
motion under a central force. He also demonstrated that if a 
body moves in an ellipse, having the centre of force at its 
focus, then the force at different points in the orbit must vary 
inversely as the square of the radius vector at those points : and 
finally, he proved that, granting the "harmonic law/' the force 
from planet to planet must also vary according to the same 
law of inverse squares. See Appendix, Art. 503. 

254. Inferences from Kepler's Laws. — From Kepler's laws 
we are therefore entitled to infer, as Newton proved, First 
(from the second law), that the force which retains the planets 
in their orbits is directed towards the sun. 

Second (from the first law), that the force which acts on 
any given planet varies inversely as the square of its distance 
from the sun. 

Third (from the "harmonic laiv"), that the force is the 
same for one planet as it would be for another in the same 
place ; or, in other words, the attracting force depends only on 
the mass and distance of the bodies concerned, and is wholly 
independent of their physical conditions (such as temperature, 
chemical constitution, etc.). It makes no sensible difference in 
the motion of a planet around the sun whether it is large or 



1 HO GRAVITATION AND THE moon's motion. [§254 
small, hot or cold, made of hydrogen or iron ; so far at least as we 

are yet able to detect. 

255. Verification of the Theory of Gravitation by the Moon's 
Motion. — When Newton first conceived the idea of " univer- 
sal gravitation " (Art. 99), he at once saw that the moon's 
motion around the earth ought to furnish a test of the theory. 
Since the moon's distance (as was even then well known) is 
about sixty times the earth's radius, the force with which it is 
"attracted" by the earth, on the hypothesis of gravitation, ought 

to be — , or - — , of what it would be if the moon were at the 
60* 3600' 

surface of the earth. Now, at the earth's surface, a body falls 

L93 inches in the first second. The moon, then, ought to fall 

towards the earth of L93 inches, or 0.0535 inches per 

3600 

second. Calculation shows that it really does 1 (sec* Appen- 
dix, Art. 505). 

The reader will notice, however, that the agreement between 

193 
the moon's " fall per second " and the — — of an inch does 
1 3600 

not establish the idea of gravitation; it only makes it probable. 

It is quite conceivable that the coincidence in this one case 

might be accidental. On the other hand, discordance would be 

absolute disproof. The complete demonstration of the law of 

gravitation Lies in its entire accordance, not with one fact, but 

with a countless multitude of them, and in its freedom from a 

single contradiction shown by the most refined observations. 

1 At the time when Newton first made the calculation, he assumed tin- 
length of a degree to be 00 miles, while as we now know, it is more than 
(51); tins made his result 16 per cent too small — so far out of the way that 
lie loyally abandoned his theory as contradicted by facts. Some years 
later when Picard's measurement of a degree in France gave a mar 
approximation to its real length, Newton at once resinned his work where 
lie had dropped it, and soon completed his theory. 



$256] 



ELLIPSE, PARABOLA, AND HYPERBOLA. 



181 



256. Newton did not rest with merely showing that the 
motion of the planets and of the moon could be explained by 
the law of gravitation, but he also solved the more general in- 
verse problem, and determined what kind of motion is required 
by that law. He found that the orbit of a body moving 
around a central mass under the law of gravitation, is not, of 
necessity a circle, nor even an ellipse of slight eccentricity 
like the planetary orbits. But it must be a " conic." Whether 
it will be circle, ellipse, parabola, or hyperbola, depends on 
circumstances. 

For a brief description of these "conies," or " conic sections " and 
the way in which they are formed by the cutting of a cone, see Appen- 
dix, Art, 506. 

257. The Ellipse, Parabola, and Hyperbola. — Fig. 67 shows 
the appearance and relation of these curves as drawn upon a 
plane. The ellipse is a " closed curve " returning into itself, 




Fig. 67 



- The Relation of the Conies to each other. 



and in it the sum of the distances of any point, N, from the 
two foci equals the major axis; i.e., FN + F 1 'N = PA. The 
hyperbola does not return into itself, but the two branches PN 1 



182 THE PROBLEM OF TWO BODIES. [§ 257 

and Pn" go off into infinity, becoming nearly straight and 
diverging from each other at a definite angle. In the hyperbola 
it is the difference of two lines drawn from any point on 
the curve to the two foci which equals the major axis : i.e., 
F"]Sr _ FN' = PA'. 

The parabola, like the hyperbola, fails to return into itself, 
but its two branches, instead of diverging, become more and 
more nearly parallel. It has but one focus and no major axis ; 
or rather, to speak more mathematically, it may be regarded 
either as an ellipse with its second focus F 1 removed to an in- 
finite distance, and therefore, having an infinite major axis; 
or with equal truth it may be considered as an hyperbola, of 
which the second focus F n is pushed indefinitely far in the 
opposite direction, so that it has an infinite negative major 
axis. 

In the ellipse, the eccentricity I — — j is less than unity. In 

the hyperbola it is greater than unity I — - j. In the parabola 

it is exactly unity ; in the circle, zero. 

The eccentricity of a conic determines its form. All circles there- 
fore have the same shape, and so do all parabolas : parabolas (when 
complete) differ from each other only in size. 

258. The Problem of Two Bodies. — This problem, proposed 
and completely solved by Newton, may be thus stated : — 

Given the masses of two spheres, and their positions and mo- 
tions at any moment; given also the law of gravitation : required 
the motion of the bodies ever afterwards, and the data necessary 
to compute their place at any future time. 

The mathematical methods by which the problem is solved 
require the use of the Calculus, and must be sought in works 
on analytical mechanics and theoretical astronomy, but the 
general results are easily understood and entirely within the 
grasp of our readers. 



§258] THE PROBLEM OF TWO BODIES. 183 

In the first place the motion of the centre of gravity of the 
two bodies is not in the least affected by their mutual attraction. 

In the next place, the two bodies will describe as orbits 
around their common centre of gravity two curves precisely 
similar in form, but of size inversely proportional to their masses, 
the form and dimensions of the two orbits being determined 
by the masses and velocities of the two bodies. 

If, as is generally the case, the two bodies differ greatly in mass, it 
is convenient to ignore the centre of gravity entirely, and to consider 
simply the relative motion of the smaller one around the centre of the 
other. It will move with reference to that point precisely as if its 
own mass, m, had been added to the principal mass, M, while it had 
become itself a mere particle. This relative orbit will be precisely 
like the orbit which m actually describes around the centre of gravity, 
except that it will be magnified in the ratio of (M+ m) to M ; i.e., if 
the mass of the smaller body is T fo of the larger one, its relative orbit 
around M will be just one per cent larger than its actual orbit around 
the common centre of gravity of the two. 

259. Finally, the orbit will always be a u conic" i.e., an 
ellipse or an hyperbola; but which of the two it will be, de- 
pends on three things, viz., the united mass of the two bodies 
(M + m), the distance r between m and M at the initial mo- 
ment, and the velocity, V, of m relative to M. If this velocity, 
V, be less than a certain critical value (which depends only on 
(M + m) and r), the orbit w r ill be an ellipse; if greater, 1 it 
will be an hyperbola. (See Appendix, Art. 507*.) 

The direction of the motion of m with respect to M, while it 
has influence upon the form and position of the orbit (its 
"eccentricity") has nothing to do with determining its species, 
and semi-major axis; nor its period in case the orbit is elliptic : 
these are all independent of the direction of m's motion. 

1 If precisely equal, the path will be a parabola, which may be regarded 
as either an ellipse or an hyperbola of infinite major axis (Art. 257). It 
is the boundary line, so to speak, between ellipses and hyperbolas. 



184 INTENSITY OF SOLAR ATTRACTION. [§259 

The problem is completely solved. From the necessary 
initial data corresponding to a given moment we can determine 
the position of the two bodies for any instant in the eternal 
past or future, provided only that no force except their mutual 
attraction acts upon them in the time covered by the calculation. 

260. Intensity of Solar Attraction. — The attraction be- 
tween the sun and the earth from some points of view appears 
like a very feeble action. It is only able to deflect the earth 
from a rectilinear course about ± of an inch in a second, dur- 
ing which time she travels more than 18 miles : and yet if it 
were attempted to replace by bands of steel the invisible grav- 
itation which draws or pushes the earth towards the sun, it 
would be necessary to cover the whole surface of the earth 
with steel wires as large as telegraph wires, and only about 
half an inch apart from each other, in order to get a connec- 
tion that could stand the strain. Such a ligament of wires 
would be stretched almost to the breaking point. The attrac- 
tion between the sun and the earth, expressed as tons of force 
(not tons of mass, of course) is 3,600,000 millions of millions 
of tons (36 with 17 ciphers). Similar stresses are acting 
through apparently empty space in all directions. 

We renew, also, the caution that the student must not think 
that the word " attraction " implies any explanation whatever, 
or any understanding of the " force " that tends to make two 
masses approach each other (see Art. 100). But this does not 
at all affect the proof and certainty of its existence. 

THE PROBLEM OF THREE BODIES: PERTURBATIONS AND 

THE TIDES. 

261. As has been said, the problem of two bodies is com- 
pletely solved ; but if instead of tivo spheres attracting each 
other we have three or more, the general problem of determin- 
ing their motions and predicting their positions transcends 
the present power of human mathematics. 



§261] THE PROBLEM OF THREE BODIES. 185 

" The problem of three bodies " is in itself as determinate 
and capable of solution as that of two. Given the initial data, 
i.e., the masses, positions, and motions of the three bodies at a 
given instant; then, assuming the law of gravitation, their 
motions for all the future, and the positions they will occupy 
at any given date are absolutely predetermined. Our present 
resources of calculation are, however, inadequate. 

But while the general problem of three bodies is intractable, 
all the particular cases of it which arise in the consideration 
of the motions of the moon and of the planets, have already 
been practically solved by special devices, Newton himself 
leading the way ; and the strongest proof of the truth of his 
theory of gravitation lies in the fact that it not only accounts 
for the regular elliptic motions of the heavenly bodies, but 
also for their apparent irregularities. 

262. It is quite beyond the scope of this work to discuss 
the methods by which we can determine the so-called " dis- 
turbing " forces and the effects they produce upon the other- 
wise elliptical motion of the moon or of a planet. We wish 
here to make only two or three remarks. 

First, that the " disturbing force " of a third body upon two 
which are revolving around their common centre of gravity is 
not the whole attraction of the third body upon either of the 
two ; but is generally only a small component of that attraction. 
It depends upon the difference of the two attractions exerted 
by the third body upon each of the pair ivhose relative motions it 
disturbs, — a difference either in intensity, or in direction, or in 
both. If, for instance, the sun attracted the moon and earth 
alike and in parallel lines, it would not disturb the moon's 
motion around the earth in the slightest degree, however pow- 
erful its attraction might be. The sun always attracts the 
moon more than twice as powerfully as the earth does ; but 
the sun's disturbing force upon the moon when at its very 
maximum is only -^ of the earth's attraction. 



186 PERTURBATIONS. [§262 

The tyro is apt to be puzzled by thinking of the earth as fixed 
while the moon revolves around it; he reasons, therefore, that at the 
time of new moon, when the moon is between the earth and sun, the 
sun would necessarily pull her away from us if its attraction were 
really double that of the earth : and it would do so if the earth were 
fixed. We must think of the earth and moon as both free to move, like 
chips floating on water, and of the sun as attracting them both witli 
nearly equal power, — the nearer of the two a little more strongly, of 
course. 

263. Second, it is only by a mathematical fiction that the 
" disturbed body " is spoken of as " moving in an ellipse " : it 
does not really do so. The path of the moon, for instance, 
never returns into itself. But it is a great convenience for the 
purposes of computation to treat the subject as if the orbit 
were a material wire always of truly elliptical form, having the 
moving body strung upon it like a bead, this orbit being con- 
tinually pulled about and changed in form and size by the 
action of the disturbing forces, taking the body with it of 
course in all these changes. This imaginary orbit at any 
moment is a true ellipse of determinable form and position, 
but is constantly changing. It is in this sense that we speak 
of the eccentricity of the moon's orbit as continually varying, 
and its lines of apsides and nodes as revolving. 

The student must be careful, however, not to let this wire theory of 
orbits get so strong a hold upon the imagination that he begins to 
think of the orbits as material things, liable to collision and destruc- 
tion. An orbit is simply, of course, the path of a body, like the track 
of a ship upon the ocean. 

264. Third, the " disturbances " and " perturbations " are 
such only in a technical sense. Elliptical motion is no more 
natural or proper to the . moon or to a planet than its actual 
motion is ; nor in a philosophical sense is the pure elliptical 
motion any more regular (i.e., "rule-following") than the so- 
called disturbed motion, 



§ 264] LUNAR PERTURBATIONS. 187 

We make the remark because we frequently meet the notion that 
the so-called "perturbations" of the heavenly bodies are imperfections 
and blemishes in the system. One good old theologian of our 
acquaintance used to maintain that they were a consequence of the 
fall of Adam. 

265. Lunar Perturbations. — The sun is the only body 
which sensibly disturbs the motion of the moon. The dis- 
turbing force due to the solar attraction is continually chang- 
ing its direction and intensity, and to attempt to trace out its 
effects would take us far beyond our purpose. We may say, 
however, that on the whole the sun's action upon the moon 
slightly diminishes the effect of the earth's attraction (by 
about ^1q) and so makes the month very nearly an hour longer 
than it otherwise would be. 

Moreover, the continual variations in the disturbing force 
are answered by a correspondingly continual writhing and 
squirming of the lunar orbit, which introduces into the lunar 
motions an almost countless number of so-called " inequali- 
ties.'' 

One or two of the largest of them, those especially which affect the 
time of eclipses, were discovered before the time of Newton ; but it is 
only within the last hundred years that the " lunar theory " has been 
brought to anything like perfection, and it is by no means " finished " 
yet : the actual place of the moon still sometimes differs from the 
almanac place by as much as 5", or say about five miles. In the 
calculation of this almanac place, over a hundred separate "inequali- 
ties " are now taken account of. 



THE TIDES. 

266. Just as the disturbing force of the sun modifies the 
intensity and direction of the earth's attraction on the moon, 
so the disturbing forces due to the attractions of the sun and 
moon act upon the liquid portions of the earth to modify the 
intensity and direction of gravity and generate the Tides, 



188 DEFINITIONS. [§266 

These consist in a regular rise and fall of the ocean surface, 
generally twice a day, the average interval between corre- 
sponding high waters on successive days at any given place 
being 24 hours, 51 minutes. This is precisely the same as the 
average interval between two successive passages of the moon 
across the meridian, and the coincidence, maintained indefi- 
nitely, of itself makes it certain that there must be some 
causal connection between the moon and the tides : as some 
one has said, the odd 51 minutes is " the moon's ear-7nark" 

That the moon is largely responsible for the tides is also 
shown by the fact that when the moon is in perigee, i.e., at the 
nearest point to the earth, they are nearly 20 per cent higher 
than when she is in apogee. The highest tides of all happen 
when the new or full moon occurs at the time when the moon 
is in perigee, especially if this perigeal new or full moon oc- 
curs about the first of January, when the earth is also nearest 
to the sun. 

267. Definitions. — While the water is rising it is "flood" 
tide ; when falling, it is " ebb." It is " high water " at the 
moment w r hen the water level is highest, and " low water " 
when it is lowest. The " spring tides " are the largest tides 
of the month, which occur near the times of new and full 
moon, while the " neap tides " are the smallest, and occur at 
half moon, the relative heights of spring and neap tides being 
about as 7 to 3. At the time of the spring tides, the interval 
between the corresponding tides of successive days is less 
than the average, being only about 24 hours, 38 minutes (in- 
stead of 24 hours, 51 minutes) and then the tides are said to 
"prime." At the neap tides, the interval is greater than the 
mean — about 25 hours, 6 minutes, and the tide "lags" The 
"establishment" of a port is the mean interval between the 
time of high water at that port and the next preceding pas- 
sage of the moon across the meridian. The " establishment " of 
New York, for instance, is 8 hours, 13 minutes ; but the actual 



§267] THE TIDE-RAISING 'FORCE. 189 

interval between the moon's transit and high water varies 
nearly half an hour on each side of this mean value at differ- 
ent times of the month, and under varying conditions of the 
weather. 

268. The Tide-Raising Force. — If we consider the moon 
alone, it appears that the effect of her attraction upon the 
earth, regarded as a liquid globe, is to distort the sphere into 
a slightly lemon-shaped form, with its long diameter pointing 
to the moon, raising the level of the water about two feet, both 
directly under the moon and on the opposite side of the earth 
(at A and B, Fig. 68), and very slightly depressing it on the 
whole great circle which lies 
half way between A and B. D 
and E are tw^o points on this 
circle of depression. 

Students seldom find any 
difficulty in seeing that the 
moon's attraction ought to 

raise the level at A) but they fig^s.— The Tides, 

often do find it very hard to 

understand why the level should also be raised at B. It seems 
to them that it ought to be more depressed just there than 
anywhere else. The mystery to them is how the moon, when 
directly under foot, can exert a lifting force such as would 
diminish one's weight. The trouble is that the student thinks 
of the solid part of the earth as fixed with reference to the 
moon, and the water alone as free to move. If this were 
the case, he would be entirely right in supposing that at B 
gravity would be increased by the earth's attraction, instead 
of diminished ; the earth, however, is not fixed, but perfectly 
free to move. 

269. Explanation and Calculation of the Diminution of 
Gravity at the Point opposite the Moon. — Consider three par- 




E 



190 



AMOUNT OF MOONS TIDE-RAISING FORCE. 



[§ 269 



tides, Fig. 69, at B, G and A, moving with equal velocities, 
Aa, Bb, and Cc, but under the action of the moon, which at- 
tracts A more powerfully than G, and B less 
so. Then if the particles have no bond of 
connection, at the end of a unit of time they 
will be at B', C, and A 1 , having followed the 
curved paths indicated. But since A is near- 
est the moon, its path will be the most curved 
of the three, and that of B the least curved. 
It is obvious, therefore, that the distances oj 
both B and A from G will have been increased; 
and if they were connected to C by an elastic 
cord, the cord ivoidd be stretched, both A and B 
being relatively pulled away from C, by prac- 
tically the same amount. We say relatively, 
because G is really pulled away from B, 
rather than B from G, — G being more at- 
tracted by the moon than B is; but the two are separated 
all the same, and that is the point. 

270. The Amount of the Moon's Tide-Raising Force. — When 

the moon is either in the zenith or nadir, the weight of a body 
at the earth's surface is diminished by about one part in eight 
and a half millions, or one pound in four thousand tons. 

At a point which has the moon on its horizon, it can be 
shown that gravity is increased by just half as much, or about 
one seventeen-millionth. 




Fig. 69. — The Tide- 
Raising Force. 



The computation of the moon's lifting force at A and B (Fig. 68) 
is as follows : The distance of the moon from the earth's centre is 
60 earth radii, so that the distances from A and B are 59 and 61 re- 
spectively. The moon's mass is about -^ of the earth's. Taking g 
for the force of gravity at the surface of the earth, we have, therefore, 



attraction of moon on A = 



80 x 59* 



-, attraction on C- 



"80 X 60 2 



, and 



attraction on B - 



!/ 



80 x 61* 



From this we find, 



$ 270] THE SUN'S TIDE-PRODUCING FORCE. 191 



8 424000' v J 8 835000 

Several attempts have been made within the last twenty years to 
detect this variation of weight by direct experiment, but so far un- 
successfully. The variations are too small. 

The moon's attraction also produces everywhere except at 
A, B, D, and E (Fig. 68) a tangential force which urges the 
particles along the surface towards the line AB, and cooperates 
in the tide-making with the radial forces above discussed. 

271. The Sun's Tide-Producing Force. — The sun acts pre- 
cisely as the moon does, but being nearly four hundred times 
as far away, 1 its tidal action notwithstanding its enormous 
mass, is less than that of the moon in the proportion (nearly) 
of 2 to 5. At new and full moon, the tidal forces of the sun 
and moon conspire, and we then have the spring tides; while 
at quadrature they are opposed and we get the neap tides. The 
relative height of the spring and neap tides has already been 
stated as about 7 to 3 {i.e., 5+2 : 5—2). 

272. The Motion of the Tides. — If the earth were wholly 
composed of water, and if it kept always the same face 
towards the moon (as the moon does towards the earth) so 
that every particle on the earth's surface were always sub- 
jected to the same disturbing force from the moon ; then, leav- 
ing out of account the sun's action for the present, a permanent 
tide would be raised upon the earth as indicated in Fig. 68. 
The difference between the level at A and D would in this 
case be a little less than tw r o feet. 

1 The " tide-producing force " of a heavenly body varies inversely as 
the cube of its distance, and directly as its mass. 



192 THE MOTION OF THE TIDES. [§ 272 

Suppose, now, the earth to be put in rotation. It is easy 
to see that the two tidal waves A and B would move over the 
earth's surface, following the moon at a certain angle depend- 
ent on the inertia of the water, and tending to move with a 
westward velocity precisely equal to that of the earth's east- 
ward rotation, — about 1000 miles an hour at the equator. 
The sun's action would produce similar tides superposed upon 
the lunar tides, and about two-fifths as large, and at different 
times of the month these two pairs of tides would be differ- 
ently related, as has already been explained, sometimes con- 
spiring, and sometimes opposed. 

If the earth were entirely covered with deep water, the tide 
waves would run around the globe regularly, and if the depth 
of water were not less than 13 miles, the tide crests, as can 
be shown (though we do not undertake it here), would follow 
the moon at an angle of just 90°. It would be high water pre- 
cisely where it might at first be supposed we should get low 
water ; the place of high water being shifted 90° by the rota- 
tion of the earth. 

If the depth of the water were, as it really is, much less 
than 13 miles, the tide wave in the ocean could not keep up 
with the moon : and this would complicate the result. More- 
over the continents of North and South America, with the 
southern Antarctic Continent, make a barrier almost complete 
from pole to pole, leaving only a narrow passage at Cape 
Horn. Consider also the varying depth of the water of the 
different oceans and the irregular contours of the shores, and 
it is evident that the whole combination of circumstances 
makes it quite impossible to determine by theory what the 
course and character of the tide waves must be. We are 
obliged to depend upon observations, and observations are 
more or less inadequate because, with the exception of a few 
islands, our only possible tide-stations are on the shores of 
continents where local circumstances largely control the 
phenomena. 






§ 273] FREE AND FORCED OS<J ILLATIONS. 193 

273. Free and Forced Oscillations. — If the water of tne 
ocean is suddenly disturbed, as for instance by an earthquake, 
and then left to itself, a " free wave " is formed, which, if the 
horizontal dimensions of the wave are large as compared with 
the depth of the water, will travel at a rate depending solely on 
the depth. 

Its velocity is equal, as can be proved, to the velocity acquired by a 
body in falling through half the depth of the ocean; 

i.e., v = ^gh, where h is the depth of the water. 

Observations upon waves caused by certain earthquakes in South 
America and Japan have thus informed us, that between the coasts of 
those countries the Pacific averages between 2| and 3 miles in depth. 

Now, as the moon in its apparent diurnal motion passes 
across the American continent each day, and comes over the 
Pacific Ocean, it starts such a " parent " wave in the Pacific, 
and a second one twelve hours later. These waves, once 
started, move on nearly (but not exactly) like a free earth- 
quake wave : not exactly, because the velocity of the earth's 
rotation being about 1050 miles an hour at the equator, the 
moon moves (relatively) westward faster than the wave can 
naturally follow it ; and so for a while the moon slightly ac- 
celerates the wave. The tidal wave is thus, in its origin, a 
" forced oscillation " : in its subsequent travel it is very nearly, 
but not entirely, " free." 

274. Co-Tidal Lines. — Co-tidal lines are lines drawn upon 
the surface of the ocean connecting points which have their 
high water at the same moment of Greenwich time. They mark 
the crest of the tide wave for every hour, and if we could map 
them with certainty, we should have all necessary information 
as to the actual motion of the tide wave. Unfortunately we 
can get no direct knowledge as to the position of these lines 
in mid-ocean : we can only determine a few points here and 



194 COURSE OF TRAVEL OF THE TIDAL WAVE. [§ 274 

there on the coasts and on the islands, so that much neces- 
sarily is left to conjecture. Fig. 70 is a reduced copy of a 
co-tidal map, borrowed by permission, with some modifications, 
from Guyot's "Physical Geography." 

275. Course of Travel of the Tidal Wave. — In studying this 
map, we find that the main or " parent " wave starts twice a day in 
the Pacific, off Callao, on the coast of South America. This is shown 
on the chart by a sort of oval " eye " in the co-tidal lines, just as on a 
topographical chart the summit of a mountain is indicated by an 
" eye " in the contour lines. From this point the wave travels north- 
west through the deep water of the Pacific, at the rate of about 850 
miles an hour, reaching Kamtchatka in ten hours. Through the shal- 
lower water to the west and southwest, the velocity is only from 400 
to 600 miles an hour, so that the wave arrives at New Zealand about 
12 hours old. Passing en by Australia, and combining with the 
small wave which the moon raises directly in the Indian Ocean, the 
resultant tide crest reaches the Cape of Good Hope in about 29 
hours, and enters the Atlantic. Here it combines with a smaller 
tide wave, 12 hours younger, which has " backed " into the Atlantic 
around Cape Horn, and it is also modified by the direct tide produced 
by the moon's action upon the Atlantic. The tide resulting from the 
combination of these three then travels northward through the Atlantic 
at the rate of nearly 700 miles an hour. It is about forty hours old 
when it first reaches the coast of the United States in Florida ; and 
our coast is so situated that it arrives at all the principal ports within 
two or three hours of that time. It is 41 or 42 hours old when it 
reaches New York and Boston. To reach London, it has to travel 
around the northern end of Scotland and through the North Sea, and 
is nearly 60 hours old when it arrives at that port, and at the ports of 
the German Ocean. 

In the great oceans, there are thus three or four tide crests travel- 
ling simultaneously, following each other nearly in the same track, 
but with continual minor changes. If we take into account the tides 
in rivers and sounds, the number of simultaneous tide crests must be 
at least six or seven ; i.e., the tidal wave at the extremity of its travel 
(up the Amazon River for instance) must be at least three or four 
days old, reckoned from its birth in the Pacific. 



196 TIDES IN RIVERS. [§ 276 

276. Tides in Rivers. — The tide wave ascends a river at a rate 
which depends upon the depth of the water, the amount of friction, 
and the swiftness of the stream. It may, and generally does, ascend 
until it comes to a rapid where the velocity of the current is greater 
than that of the wave. In shallow streams, however, it dies out ear- 
lier. Contrary to what is usually supposed, it often ascends to an eleva- 
tion far above that of the highest crest of the tide wave at the river* s mouth. 
In the La Plata and Amazon, it goes up to an elevation of at least 100 
feet above the sea level. The velocity of the tide wave in a river 
seldom exceeds 10 or 20 miles an hour, and is usually much less. 

277. Height of Tides. — In mid-ocean, the difference be- 
tween high and low water is usually between two and three 
feet, as observed on isolated islands in deep water ; but on 
continental shores the height is ordinarily much greater. As 
soon as the tide wave " touches bottom/' so to speak, the ve- 




Fig. 71. — Increase in Height of Tide on approaching the Shore. 

locity is diminished, the tide crests are crowded more closely 
together, and the height of the wave is increased somewhat as 
indicated in Fig. 71. Theoretically, it varies inversely as the 
fourth root of the depth; i.e., where the water is 100 feet deep, 
the tide wave should be twice as high as at the depth of 1600 
feet. 

Where the configuration of the shore forces the tide into a 
corner, it sometimes rises very high. At the head of the Bay 
of Fundy tides of 70 feet are said to be not uncommon, and 
some of nearly 100 feet have been reported. 

278. Effect of the Wind, and Changes in Barometric Pressure. 

— When the wind blows into the mouth of a harbor, it drives in the 
water by its surface friction, and may raise the level several feet. In 
such cases the time of high water, contrary to what might at first be 



§278] TIDES IN LAKES AND INLAND SEAS. 197 

supposed, is delayed, sometimes as much as 15 or 20 minutes. This 
depends upon the fact that the water runs into the harbor for a longer 
time than it would do if the wind were not blowing. 

When the wind blows out of the harbor, of course there is a corre- 
sponding effect in the opposite direction. 

When the barometer at a given port is lower than usual, the level of 
the water is usually higher than it otherwise would be, at the rate of 
about one foot for every inch of difference between the average and 
actual heights of the barometer. 

279. Tides in Lakes and Inland Seas. — These are small and 
difficult to detect. Theoretically, the range between high and low 
water in a land-locked sea should bear about the same ratio to the rise 
and fall of tide in mid-ocean that the length of the sea does to the 
diameter of the earth. On the coasts of the Mediterranean the tide 
averages less than 18 inches, but it reaches the height of three or 
four feet at the head of some of the gulfs. In Lake Michigan, at 
Chicago, a tide of about If inches has been detected, the " establish- 
ment " of Chicago being about 30 minutes. 

280. Effects of the Tides on the Rotation of the Earth. — 

If the tidal motion consisted merely in the rising and falling of the 
particles of the ocean to the extent of some two feet twice daily, it 
would involve a very trifling expenditure of energy ; and this is the 
case with the mid-ocean tide. But near the land this slight oscillatory 
motion is transformed into the bodily travelling of immense masses 
of water, which flow in upon the shallows and then out again to sea 
with a great amount of fluid friction ; and this involves the expendi- 
ture of a very considerable amount of energy. From what source 
does this energy come ? 

The answer is that it must be derived mainly from the earth's 
energy of rotation, and the necessary effect is to lessen the speed of 
rotation, and to lengthen the day. Compared with the earth's whole 
stock of rotational energy, however, the loss by tidal friction even in 
a century is very small, and the theoretical effect on the length of the 
day extremely slight. Moreover, while it is certain that the tidal 
friction, by itself considered, lengthens the day, it does not follow that 
the day grows longer. There are counteracting causes, — for in- 
stance, the earth's radiation of heat into space and the consequent 



198 



EFFECT OF TIDE ON MOON S MOTION. 



[§ 280 



shrinkage of her volume. At present we do not know as a fact 
whether the day is really longer or shorter than it was a thousand 
years ago. The change, if real, cannot well be as great as T7 Vo °f a 
second. 



281. Effect of the Tide on the Moon's Motion. — Not only 

does the tide diminish the earth's energy of rotation directly by the 
tidal friction, but theoretically it also communicates a minute portion 
of that energy to the moon. It will be seen that 
a tidal wave situated as in Fig. 72 would slightly 
accelerate the moon's motion, the attraction of 
the moon by the tidal protuberance, F, being 
slightly greater than that of the opposite wave 
at F' . This difference would tend to draw it 
along in its orbit, thus slightly increasing its 
velocity, and so indirectly increasing the major 
axis of the moon's orbit, as well as its pe- 
riod. The tendency is, therefore, to make the 
moon recede from the earth and to lengthen the 
month. 

Upon this interaction between the tides and 
the motions of the earth and moon, Prof. George 
Darwin has founded his theory of "tidal evolu- 
tion" viz., that the satellites of a planet, having 
separated from it millions of years ago, have 
been made to recede to their present distances 
by just such an action. An excellent popular 
statement of this theory will be found in the 
closing chapter of Sir Robert Ball's " Story of the Heavens." 




Fig. 72. 

Effect of the Tide on 
the Moon's Motion. 



282] THE PLANETS IN GENERAL. 199 



CHAPTER X. 

THE PLANETS IN GENERAL. 

BODE'S LAW. — THE APPARENT MOTIONS OF THE PLAN- 
ETS. — THE ELEMENTS OF THEIR ORBITS. — DETERMI- 
NATION OF PERIODS AND DISTANCES. — STABILITY OF 
THE SYSTEM. — DETERMINATION OF THE DATA RELAT- 
ING TO THE PLANETS THEMSELVES. — DIAMETER, MASS, 
ROTATION, SURFACE-CHARACTER, ATMOSPHERE, ETC. — 
herschel's ILLUSTRATION OF THE SCALE OF THE 
SYSTEM. 

282. The stars preserve their relative configurations, how- 
ever much they alter their positions in the sky from hour to 
hour. The Dipper remains always a " Dipper " in every part 
of its diurnal circuit. But certain of the heavenly bodies, 
and among them the most conspicuous, behave differently. 
The sun and moon continually change their places, moving 
always eastward among the constellations ; and a few others, 
which to the eye appear as very brilliant stars (really not 
stars at all), also move, 1 though not in quite so simple a way. 

These moving bodies were called by the Greeks "planets'* ; 
i.e., "wanderers." The ancient astronomers counted seven of 
them, — the sun and the moon, and in addition Mercury, 
Venus, Mars, Jupiter, and Saturn. At present, the sun and 

1 When we speak of the " motion " of the planets, the reader will un- 
derstand that the apparent diurnal motion is not meant. We refer to 
their motions among the stars; i.e., their change of right ascension and 
declination. 



200 DISTANCES OF THE PLANETS FEOM THE SUN. [§ 282 

moon are not reckoned as planets, but the roll includes, in addi- 
tion to the live other bodies known to the ancients, the earth 
itself, which Copernicus showed should be counted among 
them, and also two new bodies (Uranus and Neptune) of great 
magnitude, though inconspicuous because of their distance. 
Then there is, in addition, the host of the so-called asteroids. 

283. The list of the planets in the order of their distance 
from the sun stands thus at present, — Mercury, Venus, the 
Earth, Mars, Jupiter, Saturn, Uranus, and Neptune ; and between 
Mars and Jupiter, where another planet would naturally be ex- 
pected, there have already been discovered between 400 and 500 
little planets, or " asteroids" which probably represent a single 
planet somehow either " spoiled in the making," so to speak, 
or else subsequently burst into fragments. These planets are 
all (probably) dark bodies, shining only by reflected light, — 
globes which, like the earth, revolve around the sun in orbits 
nearly circular, moving all of them in the same direction, and 
(with some exceptions among the asteroids) nearly in the 
common plane of the ecliptic. All but the inner two and the 
asteroids are attended by " satellites." Of these the earth has 
one (the moon), Mars two, Jupiter five, Saturn eight, Uranus 
four, and Neptune one. 

284. Relative Distances of the Planets from the Sun ; Bode's 
Law. — There is a curious approximate relation between the 
distances of the planets from the sun, usually known as 
" Bode's Law" 

It is this : Write a series of 4 ? s. To the second 4 add 3, to 
ohe third, add 3 X 2, or 6 ; to the fourth, 4 x 3, or 12 ; and so on, 
doubling the added number each time, as in the following scheme. 



4 


4 


4 


4 


4 


4 


4 


4 


4 




3 


6 


12 


24 


48 


9(5 


192 


384 


1 


7 


10 


16 


[28] 


52 


100 


190 


388 


V 


9 


e 


S 


® 


V 


h 


¥ 


V 



284] 



TABLE OF NAMES, DISTANCES, ETC. 



201 



The resulting numbers (divided by 10) are approximately 
equal to the true mean distances of the planets from the sun, 
expressed in radii of the earth's orbit (astronomical units) ; 
— excepting Neptune however; in his case the law breaks down 
utterly. For the present, at least, it is to be regarded as a 
mere coincidence, rather than a real " law." ]So satisfactory 
explanation of it has yet been found. 

285. Table of Names, Distances, and Periods. 



Name. Symbol. 


Distance. 


Bode. 


DlFF. 


Sid. Period. 


Syn. 
Period. 


Mercury .... 

Venus 

Earth 

Mars 


e 
$ 


0.387 
0.723 
1.000 
1.523 


0.4 
0.7 
1.0 
1.6 


-0.013 

+ 0.023 

0.000 

- 0.077 


88 d or 3 mo - 
224.7 d or 7J mo - 
3651 d or V 
687 d or 17 10 mo - 


116 d 
584 d 

780 d 


Mean Asteroid 


2.650 


2.8 


- 0.150 


3^.1 to 8^.0 


various 


Jupiter .... 

Saturn 

Uranus .... 
Neptune .... 




5.202 

9.539 

19.183 

30.054 


5.2 
10.0 
19.6 
38.8 


+ 0.002 

- 0.461 
-0.417 

- 8.746 ! 


lly.9 

293.5 

843-.0 

164^.8 


399 d 
378 d 
370 d 
367£ d 



The column headed "Bode" gives the distance according to Bode's 
law ; the column headed " Diff.," the difference between the true distance 
and that given by Bode's law. 

Fig. 73 shows the smaller orbits of the system (including 
the orbit of Jupiter), drawn to scale, the radius of the earth's 
orbit being taken as one centimetre. On this scale the di- 
ameter of Saturn's orbit would be 19 cm .08, that of Uranus 
would be 38 cm .36, and that of Neptune 60 cm .ll, or about 2 
feet. The nearest fixed star, on the same scale, would be 
about a mile and a quarter away. It will be seen that the 
orbits of Mercury, Mars, Jupiter, and several of the asteroids 
are quite distinctly " out of centre w with respect to the 
sun. 



202 



PERIODS. 



[§286 



286. Periods. — The Sidereal Period of a planet is the time 
of its revolution around the sun, from a star to the same star 
again, as seen from the sun. The Synodic Period is the time 
between two successive conjunctions of the planet with the 
sun, as seen from the earth. 




Fig. 73. — Plan of the Smaller Planetary Orbits. 

The sidereal and synodic periods are connected by the same rela- 
tion as the sidereal and synodic months (Art. 141), namely, 

S P E' 



§286] APPARENT MOTIONS. 203 

in which E, P, and S are respectively the periods of the earth and of 
the planet, and the planet's synodic period, and the numerical differ- 
ence between — and — is to be taken without regard to sign ; i.e., for 
P E 

an inferior planet, - = ; for a superior one, — = . The 

S P E SEP 

two last columns of the table of Art. 285 give the approximate 
periods, both sidereal and synodic, for the different planets. 

287. Apparent Motions. — If we imagine a line drawn 
through the sun perpendicular to the plane of the ecliptic, the 
planets, from a distant point on this line, would be seen to 
travel in their nearly circular orbits with a steady, forward 
motion; but viewed from the earth, the apparent motion is 
complicated, being made up of their own real motion around 
the sun, combined with an apparent motion due to the earth's 
own movement. 

The apparent motion of a body relative to the earth can be 
very simply stated. Every body which is really at rest will 
appear, as seen from the earth, to move in an orbit identically 
like the earth's orbit, and parallel to it, but keeping in such a 
part of this apparent orbit as always to have its motion precisely 
equal and opposite the earth's own real motion at the moment. 
If a body is really moving, its apparent motion with respect 
to the earth will be found by combining its motion with an- 
other motion equal to that of the earth, but reversed. It is not 
difficult to prove this, but our space will not permit. 

288. Effect of the Combination of the Earth's Motion with 
that of a Planet. — The apparent or "geocentric" motion of a 
planet is therefore made up of two motions, and appears to be 
that of a body moving once a year around the circumference 
of a circle equal to the earth's orbit, while the centre of 
this circle itself goes around the sun upon the real orbit 
of the planet, and with a periodic time equal to that of the 
planet. 



204 



EXPLANATION OF TERMS. 



[§288 



Jupiter, for instance, appears to move as in Fig. 74, making 11 
loops in each revolution, the smaller circle having a diameter of about 

one-fifth of the larger one, upon 
which its centre moves, since 
the diameter of Jupiter's orbit 
is about live times that of the 
earth. 

As a consequence, we 
have an apparent back-and- 
forth movement of the 
planets among the stars. 
They move eastward (tech- 
nically " advance ") part of 
the time, and part of the 
time they move westward 
(technically "retrograde "), 
the arc of retrogression be- 
ing, however, always less than that of advance. 




Pie. 74. 

Apparent Gfooce&trio Motion of Jupiter. 



289. Explanation of Terms. — Fig, 75 illustrates the mean- 
ing of a number of terms which arc used in describing a 
planet's position with reference to the sun, viz.. Opposition, 
Quadrature, Inferior and Superior Conjunction,} and Greatest 
Elongation. E is the position of the earth, the inner circle 
being the orbit of an "inferior" planet, while the outer circle 
is the orbit o{ a "superior" planet. Tn general, the angle 
PES (the angle at the earth between lines drawn from the 
earth to the planet and the sun) is the planet's elongation. 
For a superior planet, it can have any value from zero to 180°; 
for an inferior, it has a maximum value that the planet can- 
not exceed, depending upon the diameter of its orbit. 



290. Motion of a Planet in Right Ascension and Longitude. 

— Starting from the line o( superior conjunction, the planet whether 
superior or inferior, moves eastward or "direct" for a time, but at a 



§290] 



MOTION OF THE PLANETS. 



205 



rate continually slackening until the planet becomes " stationary " ; 
then it reverses its course and moves westward, the middle of the arc 
of retrogression always coinciding with the point where it comes to 
opposition or Inferior conjunction. After a time it becomes once 
more stationary, and then resumes its eastward motion until it again 
arrives at superior conjunction, having completed a synodic period. 
In time, as well as in degrees, the " advance " always exceeds the 
" retrogression." 

As observed with a sidereaj, clock, all the planets come later to the 
meridian each night when moving direct, since their right ascension is 
then increasing ; vice versa, of course, when they are retrograding. 

Conjunction 




Opposition 

Fig. 75. — Planetary Configurations and Aspects. 



291. Motion of the Planets with respect to the Sun's Place in 
the Sky; Change of Elongation. — The visibility of a planet 
depends mainly on its "elongation " (i.e., its angular distance 
from the sun), because when near the sun, the planet will be 
above the horizon only by day. As regards their motion, eon- 



206 MOTION OF THE PLANETS. [§ 201 

sidered from this point of view, there is a marked difference 
between the inferior planets and the superior. 

I. The superior planets drop always steadily westward with 
respect to the sun's place in the heavens, continually increasing 
their western elongation or decreasing their eastern. As ob- 
served by an ordinary time-piece (keeping solar time), they 
therefore invariably come earlier to the meridian every succes- 
sive night, never moving eastward among the stars as rapidly 
as the sun does. 

Beginning at conjunction, the planet is then behind the sun, at its 
greatest distance from the earth, and invisible. It soon, however, 
reappears in the morning, rising before the sun, and passes on to 
western quadrature, .when it rises at midnight. Thence it moves on 
to opposition, when it is nearest and brightest, and rises at sunset. 
Still dropping westward and receding, it by and by reaches" eastern 
quadrature and is on the meridian at sunset. Thence it still crawls 
sluggishly westward until it is lost in the evening twilight and com- 
pletes its synodic period by again reaching conjunction. 

292. II. The inferior planets, on the other hand, apparently 
oscillate across the sun, moving out equal distances on each side 
of it, but making the westward swing much more quickly than 
the eastward. 

At superior conjunction an inferior planet is moving eastward faster 
than the sun. Accordingly it creeps out into the twilight as an even- 
ing star, and continues to increase its apparent distance from the sun 
until it reaches its " greatest eastern elongation " (47° for Venus ; for 
Mercury, from 18° to 28°). Then the sun begins to gain upon it, and 
as the planet itself soon begins to retrograde, the elongation diminishes 
rapidly, and the planet rushes back towards inferior conjunction, passes 
it, and, as a morning star, moves swiftly out to its western elongation. 
Then it turns and climbs slowly back to superior conjunction again. 

293. Motions in Latitude. — If the planets' orbits lay precisely 
in the same plane with each other and with the earth's orbit, they 
would always keep exactly in the ecliptic ; but while they never go 
far from that circle, they do, in fact, deviate a few degrees from it, so 



293] 



MOTIONS IN LATITUDE. 



207 



that their paths in the heavens form more or less complicated loops and 
kinks. Fig. 75* shows the loops made by Satnrn and Uranns in 1897. 




Fig. 75*. — Motion of Saturn and Uranus in 1897. 

294. Ptolemaic System. — Assuming the fixity and central posi- 
tion of the earth and the actual revolution of the heavens, Ptolemy, 
who flourished at Alexandria about 140 a.d., worked out the system 
which bears his name. In his great work, the Almagest, which for 
14 centuries was the authoritative "Scripture of Astronomy," he 
showed that all the apparent motions of the planets, so far as then 
observed, could be accounted for by supposing each planet to move 
around the circumference of a circle called the " epicycle" while the 
centre of this circle, sometimes called the " fictitious planet," itself 
moved around the earth on the circumference of another and larger 
circle called the "deferent" To account for some of the irregularities 
of the planets, however, it was necessary to suppose that both the 
deferent and epicycle, though circular, are eccentric. 

295. The Copernican System. — Copernicus (1473-1543) as- 
serted the diurnal rotation of the earth on its axis, and showed 
that this would fully account for the apparent diurnal revo- 
lution of the heavens. He also showed that nearly all the 



208 ELEMENTS OF A PLANET'S ORBIT. [§ 295 

known motions of the planets could be accounted for by sup- 
posing them to revolve around the sun (with the earth as one 
of them) in orbits circular, but slightly out of centre. His 
system, as he left it, was very nearly that which is accepted 
to-day, and Fig. 73 may be taken as representing it. He was 
obliged, however, to retain a few small epicycles to account 
for certain of the irregularities. 

So far, no one had dared to doubt the exact circularity of the 
celestial orbits. It was considered metaphysically improper 
that heavenly bodies should move in any but perfect curves, 
and no curve but the circle was recognized as such. It w~as 
left for Kepler, some 65 years later than Copernicus, to show 
that the planetary orbits are elliptical, and to bring the system 
substantially into the form in which we know it now. 

296. The Elements of a Planet's Orbit are a set of numer- 
ical quantities, seven in number, which embody a complete 
description of the orbit, and supply the data for the prediction 
(perturbations excepted) of the planet's exact place at any 
time in the past or future. 

An explanation of them will be found in the Appendix, 
Art. 507. 

There is a general method, the discussion of which lies quite beyond 
our reach, by which all the seven elements of a planet's orbit can be 
deduced from any three perfectly accurate observations of the right 
ascension and declination of the body, separated by a few weeks' inter- 
val (excepting, however, one or two special cases where the observed 
places are so peculiarly situated that a fourth observation becomes 
necessary). Of course, if the observations are not perfect, and they 
never are, the orbit deduced will be only approximate ; but in ordinary 
cases three observations such as are now usually made at our standard 
observatories, with an interval of a month or so between the extremes, 
will give a very fair approximation to the orbit, which can then be 
corrected by farther observation. This general method of computing 
the orbit from three observations was invented in 1801, by Gauss, 
then a young man of 23, in connection with the discovery of Ceres, 



§296] planet's period. 209 

the first of the asteroids, which, after its discovery by Piazzi, was soon 
lost to observation in the rays of the sun. 

Since, however, the planetary orbits are for the most part 
approximately circular, and nearly in the plane of the ecliptic, 
they are described with sufficient accuracy for many purposes 
by giving simply the planet's mean distance from the sun with 
the corresponding period. 

297. Determination of a Planet's Sidereal Period. — This 
may be effected by determining the mean synodic period of 
the planet from a comparison of the dates of two oppositions, 
widely separated in time, if possible. The exact instant of 
opposition is found from a series of right ascensions and dec- 
linations observed about the proper date ; and by comparing 
the deduced longitudes with the corresponding longitudes of 
the sun, we easily find the precise moment when the difference 
was 180°. When the synodic period is found, the sidereal is 

given by the equations of Art. 286, viz., — = for an 

S P E 

inferior planet and - = for a superior one. In the first 

case, P = ; in the second, . It will not answer for 

: S+E* 9 S-E m 

this purpose to deduce the synodic period from two successive 
oppositions, because, on account of the eccentricity of the 
orbits, both of the planet and of the earth, the synodic peri- 
ods are somewhat variable. The observations must be suffi- 
ciently separated in time to give a good determination of the 
mean synodic period. 

298. Geometrical Method of Determining a Planet's Distance 
in Astronomical Units. — When we have found the planet's 
sidereal period, we can easily ascertain its distance from the 
sun in astronomical units by means of two observations of 
its elongation from the sun, made at two dates separated by an 
interval of exactly one of its periods. 



210 



planet's distance from sun. 



[§298 



The " elongation," it will be remembered, is the difference between 
the longitude of the planet and that of the sun as seen from the earth, 
and is determined for any given instant by means of a series of 
meridian-circle observations of both sun and planet covering the 
desired date. 

299. To find the distance of Mars, for instance, we must 
have two elongations observed at an interval of 687 (686.95) 
days, so that the planet at the second observation will be at 
the same point, M, (Fig. 76) which it occupied at first. If the 

■4 ^ 




Fig. 76. — Determination of the Distance of a Planet from the Sun. 

earth was at A at the first observation, then at the second she 
will be at a point, C, so situated that the angle ASC will be 
that which the earth will describe in the next 43^ days (the 
difference between 687 days and two complete years) and is 



§ 299] 



planet's distance from sun. 



211 



therefore known. The two angles SAM and SCM are the two 
elongations of the planet, given directly by the observations. 
The two sides SA and SC are also known, being the earth's 
distance from the sun at the two times of observation. Hence, 
knowing two adjacent sides of the quadrilateral and its angles, 
we can easily solve it (as in Art. 149), and find SM, and also 
the angle ASM or CSM, which determines the direction of M 
from S at that point in its orbit. 

The student can follow out for himself the process by which, from 
two elongations of Venus, SA V and SBV, observed at an interval of 
225 days, SFcan be determined. 

300. From a sufficient number of sucli pairs of observations 
distributed around the planet's orbit, it will evidently be pos- 
sible to work out completely the magnitude and form of the 
orbit, and it was actually in just this way that Kepler, from 
the observations of Tycho, showed that the planetary orbits 
are ellipses, and deduced their relative distances from the sun 
as compared with that of the earth. His harmonic law was 
then discovered by simply comparing the periods with the dis- 
tances. Now that we have 
the "harmonic law," a plan- 
et's approximate mean dis- 
tance can, of course, be much 
more easily found by apply- 
ing the law (the period being 
given) than by the geometri- 
cal method. 




301 . Simple Method of find- 
ing the Distance of an Infe- 
rior Planet. —In the case of Distance of an Inferior Planet determined by 



Fig. ' 



Venus, which has a practically 
circular orbit, the method illus- 
trated by Fig. 77 may be used. 



Observations of its Greatest Elongation. 



When the planet is at its greatest 



elongation, the angle SVE is sensibly a right angle, so that we need 



212 PLANETARY PERTURBATIONS. [§ 301 

only to know SE and the angle of greatest elongation, ESV, in order 
to compute SV. Mercury's orbit is so eccentric that the method in 
his case will give only rough approximations. 

302. Planetary Perturbations. — The attractions of the plan- 
ets for each other disturb their otherwise elliptical motion 
around the sun, somewhat as the sun disturbs the motion of 
the moon around the earth ; but the disturbing forces are in 
nearly all cases small, and the resulting perturbations, as a 
rule, are much less than in the case of the moon. They are 
divided into two great classes, — the periodic and the secular. 

303. Periodic Perturbations. — The periodic are such as de- 
pend upon the relative positions of the planets in their orbits, 
and generally run through their course in less than a century, 
though there are some with periods exceeding a thousand 
years. For the most part they are trifling in amount. 

Those of Mercury never exceed 15", as seen from the sun. Those 
of Venus may reach 30"; those of the earth about 1'; and those of 
Mars a little over 2'. The mutual disturbances of Jupiter and Saturn 
are much larger, reaching 28' and 48' respectively. Those of Uranus 
never exceed 3', and those of Neptune are smaller yet. In the case 
of asteroids, however, disturbed by Jupiter, the displacement is some- 
times enormous, as much as 8° or 10°. 

304. Secular Perturbations. — These are such as depend 
not on the positions of the planets in their orbits, but on the 
relative positions of the orbits themselves. Since these positions 
change very slowly, these perturbations, though in the strict 
sense periodic also, are extremely slow in their develop- 
ment, running along, as the name implies, "from age to age," 
in periods to be reckoned only by myriads and millions of 
years. 

The major axes and periods of the orbits are never altered 
by these secular perturbations, a most remarkable fact, first 



§304] STABILITY OF THE PLANETARY SYSTEM. 213 

proved by La Place and La Grange about a century ago. 
These two elements, though subject to slight periodical ine- 
qualities, are absolutely constant in the long run, so far as the 
effects of planetary perturbations are concerned. 

The nodes x and perihelia, on the other hand, move around continu- 
ously. All the nodes regress, and all the lines of apsides advance (that 
of Venus alone excepted). The shortest of their periods of revolu- 
tion is 37,000 years, the longest over half a million. 

The inclinations of the orbits to the plane of the ecliptic oscillate 
back and forth, in periods (not regular, however) of many thousand 
years, but the oscillations are confined within a very few degrees. 

The eccentricities also oscillate back and forth in a similar way, alter- 
nately increasing and decreasing, but only within narrow limits. 

305. Stability of the Planetary System. — The solar system, 
therefore, is not exposed to serious derangement as the result 
of the mutual attraction of the planets. The mean distance 
and period of every orbit is unalterable in the long run ; the 
changes in the position of node and perihelion are of no con- 
sequence, and the alterations in the inclination and eccen- 
tricity, which would be serious if they were extensive, are 
confined within narrow limits. The system in itself is stable. 

It does not follow, however, that because the mutual attrac- 
tions of its members cannot seriously derange the system, 
there may not be other causes which can do so. There are 
many conceivable actions which would necessarily terminate 
in its destruction, such as the retardation of planetary motions 
which would be caused by a resisting medium, or by the en- 
counter with a sufficiently dense swarm of meteoric matter. 
We add also that the asteroids have not the same guarantees 
of safety as the larger planets. The changes of their inclina- 
tions and eccentricities are not narrowly limited. 

1 The nodes of a planet's orbit are the points where their orbits cut the 
cliptic, like the nodes of the moon's orbit (Art. 142). The perihelia are the 
points nearest the sun. 



214 THE PLANETS THEMSELVES. [§300 



THE PLANETS THEMSELVES. 

306. In studying the planetary system, we meet a number 
of subjects of inquiry which refer to the individual planet, 
and not at all to its orbit, — such, for instance, as its magni- 
tude; its mass, density, and surface gravity ; its axial rotation 
and ellipticity ; its brightness, phases, an( l reflecting power or 
u albedo" and the spectroscopic qualities of its light; its atmos- 
phere ; its surface-markings and topography; and, finally, its 
satellite system. 

307. Magnitude. — The size of a planet is found by measur- 
ing its angular diameter with some form of micrometer (see 
Appendix, Art. 542). Since we can find the distance of a 
planet from the earth at any moment when we know the ele 
ments of its orbit, this will give us the means of finding at 
once the planet's linear diameter. It will come out in astro- 
nomical units (i.e., in terms of the earth's mean distance from 
the sun) if the planet's distance is expressed in such units : if 
we know the value of that unit (about 93,000000 miles), which 
depends upon our knowledge of the solar parallax, then we 
can also find the planet's diameter in miles. 



The equation is simply 

d" 



Linear diameter = D X 



206265 



in which D is the distance of the planet from the earth, and d n the 
number of seconds of arc in its measured diameter. 

308. It is customary to divide the real semi-diameter or 
radius of the planet by that of the earth, and call the quotient 
r (i.e., r is the number of times the planet's semi-diameter 
exceeds that of the earth). The area of the planet's surface 
(compared with that of the earth) then equals r 2 , and its 
volume or bulk equals r 3 . 



§ 308] MASS. DENSITY, AND SURFACE GRAVITY. 215 

If, as is nearly the case with Jupiter, the diameter is eleven times 
that of the earth, r=ll; the surface of Jupiter = r 2 = 121, and the 
volume = r 3 = 1331 times that of the earth. 

The nearer the planet, other things being equal, the more 
accurately r and the quantities derived from it can be deter- 
mined. An error of O'M in measuring the apparent diameter 
of Venus when nearest counts for less than 13 miles, while 
in Neptune's case it would correspond to more than 1300. 

309. Mass, Density, and Surface Gravity. — If the planet 
has a satellite, its mass is very easily and accurately found 
from the proportion l 

J? .a? 

T 2 ' t 2 



Mass of sun : mass of planet : . 



in which A is the mean distance of the planet from the sun 
and T its sidereal period of revolution ; while a is the distance 
of the satellite from the planet, and t its sidereal period. 

Substantially the same proportion may be used to compare 
the planet with the earth, viz., 



a? a<? 



Earth + moon -.planet + satellite '•:—„• 

a and t being here the distance and period ol! the moon, and 
a 2 and t 2 those of the planet's satellite. 

For a demonstration of these proportions, see Appendix, Art. 508. 
When a planet has no satellite its mass can be determined only by 
means of the perturbations which it produces in the motion of othei 
planets, or of comets. 



1 The proportion given is not absolutely correct. Strictly the first 
ratio of the proportion should he 

Mass of sun + planet : mass of planet + satellite ; 

and moreover, the T and t used must be, not exactly the actual periods, 
but the periods cleared of perturbations ; the difference in the result is, how- 
ever, insignificant, except in cases involving the earth and moon. 



216 DATA RELATING TO THE PLANET'S LTGHT. [§309 

Having the planet's mass compared with the earth, we get 
its density by dividing the mass by the volume ; i.e., 

Density = -. 
r 

The superficial gravity, i.e., the force of gravity on the plan- 
et's surface compared with that of the earth (neglecting the 

centrifugal force due to its rotation) is simply — . 

310. The Rotation Period and Data connected with it. — 

The length of the planet's day, when it can be determined at 
all, is ascertained by observing some spot upon the planet's 
disc, and noting the interval between its returns to the same 
apparent position. 

In reducing the observations, account has to be taken of the con- 
tinual change in the direction of the planet from the earth, and also 
of the variations of its distance, which alter the time taken by light 
in reaching us. 

The inclination of the planet's equator to the plane of its 
orbit, and the position of its equinoxes, are deduced from the 
same observations that give the planet's rotation period ; we 
have to observe the path pursued by a spot in its hiotion 
across the disc. Only Mars, Jupiter, and Saturn permit us to 
find these elements of their rotation with any considerable 
accuracy. 

The " ellipticity" " oblateness" (Art. 90) or "polar compres- 
sion " of the planet, due to its rotation, is found by micromet- 
ric measures of its polar and equatorial diameters. 

311. Data relating to the Planet's Light. — The planet's 
brightness, and its reflecting power or " albedo" are deter- 
mined by photometric observations ; and the spectroscopic 
peculiarities of its light are, of course, studied with the spec- 
troscope. The question of its atmosphere is investigated also 



§ 311] SATELLITE SYSTEM. 217 

by means of various effects upon the planet's appearance and 
light. The planet's surface-markings and topography are stud- 
ied directly with the telescope, by making careful drawings 
of the appearances noted at different times. If the planet has 
any well marked and characteristic spots upon it, by which 
the time of rotation can be found, then it soon becomes easy 
to identify such as are really permanent, and after a time to 
chart them more or less perfectly ; but we add immediately, 
that Mars is the only planet of which, so far, we have been 
able to make anything which can be called a map. 

312. Satellite System. — The principal data to be ascer- 
tained are the distances and the periods of the satellites. 
These are obtained by micrometric measures of the apparent 
distance and direction of each satellite from the planet, but the 
reduction of the observations is rather complicated on account 
of the continual change in the planet's distance and direction 
from the earth. 

In a few cases, also, it is possible to make observations by which 
we can determine the diameter of the satellites ; and where there are 
a number together, their masses may sometimes be ascertained from 
their mutual perturbations. 

With the exception of our moon and Iapetus, the outer sat- 
ellite of Saturn, all the satellites of the solar system move 
almost exactly in the plane of the equator of the planet to 
which they belong ; at least, so far as known, for we do not 
know with certainty the position of the equatorial planes of 
Uranus and Neptune. Moreover, all the satellites but the 
moon and Hyperion, the seventh satellite of Saturn, move in 
orbits that are practically circles. 

313. Classification of Planets. — Humboldt has classified 
the planets in two groups, — the " terrestrial planets" as he 
calls them, and the " major planets" The terrestrial group 



218 



CLASSIFICATION OF PLANETS. 



[§313 



contains the four planets nearest the sun, — Mercury, Venus, 
the Earth, and Mars. They are all bodies of similar magni- 
tude, ranging from 3000 to 8000 miles in diameter ; not very 
different in density and probably roughly alike in physical 
constitution, though probably also differing very much in the 
extent, density, and character of their atmospheres. 

The four major planets, Jupiter, Saturn, Uranus, and Nep- 
tune are much larger bodies, ranging from 32,000 to 90,000 
miles in diameter ; are much less dense ; and, so far as we can 




Fig. 78. — Relative Sizes of the Planets. 

make out, present only cloud-covered surfaces to our inspec- 
tion. There are strong reasons for supposing that they are at 
a high temperature, and that Jupiter especially is a sort of 
"semi-sun" ; but this is not certain. 

As to the asteroids, the probability is that they represent a 
fifth planet of the terrestrial group, which, as has been already 
intimated, failed somehow in its evolution, or else has been 
broken to pieces. 



§ 313] herschel's illustration. 219 



Fig. 78 gives an idea of the relative sizes of the planets. The 
sun on the scale of the figure would be about a foot in diameter. 

314. Tables of Planetary Data. — In the Appendix we present 
tables of the different numerical data of the solar system, derived 
from the best authorities and calculated for a solar parallax of S".80, 
the sun's mean distance being, therefore, taken as 92,897,000 miles. 
These tabulated numbers, however, differ widely in accuracy. The 
periods of the planets and their distances in astronomical units are very 
precisely known : probably the last decimal place in the table may 
be trusted. ~Next in certainty come the masses of such planets as have 
satellites, expressed in terms of the sun's mass. The masses of Venus 
and Mercury, however, are much more uncertain. The distances of 
the planets in miles, their masses in terms of the earth's mass, and their 
diameters in miles, all involve the solar parallax, and are affected by 
the slight uncertainty in its amount. For the remoter planets, more- 
over, diameters, volumes, and densities are subject to a very consider- 
able percentage of error, as explained above. The student need not 
be surprised, therefore, at finding serious discrepancies between the 
values given in these tables and those given by others, amounting in 
some cases to 10 per cent or 20 per cent, or even more. Such differ- 
ences merely indicate the actual uncertainties of our knowledge. 

315. Sir John Herschel's Illustration of the Dimensions of 
the Solar System. — In his " Outlines of Astronomy," Herschel 
gives the following illustration of the relative magnitudes and dis- 
tances of the members of our system : — 

" Choose any well-levelled field. On it place a globe two feet in diameter. 
This will represent the sun. Mercury will be represented by a grain of mus- 
tard seed on the circumference of a circle 164 feet in diameter for its orbit ; 
Venus, a pea, on a circle of 284 feet in diameter; the Earth, also a pea, on a 
circle of 430 feet ; Mars, a rather large pin's head, on a circle of 654 feet ; the 
asteroids, grains of sand, on orbits having a diameter of 1000 to 1200 feet ; 
Jupiter, a moderate-sized orange, on a circle nearly half a mile across; Sat- 
urn, a small orange, on a circle of four-fifths of a mile; Uranus, a full-sized 
cherry or small plum, upon a circumference of a circle more than a mile in 
diameter; and, finally, Neptune, a good-sized plum, on a circle about 2| miles 
in diameter." 

We may add that on this scale, the nearest star would be on the 
opposite side of the earth, 8000 miles away. 



220 THE INDIVIDUAL PLANETS. [§ 316 



CHAPTER XI. 

THE TERRESTRIAL AND MINOR PLANETS. 

316. Mercury lias been known from the remotest anti- 
quity. At first, astronomers failed to recognize it as the same 
body on the eastern and western side of the sun, and among 
the Greeks it had for a time two names, — Apollo, w T hen it 
was morning star, and Mercury, when it was evening star. It 
is so near the sun that it is comparatively seldom seen with 
the naked eye, but when near its greatest elongation it is 
easily enough visible as a brilliant star of the first magnitude, 
low down in the twilight. It is best seen in the evening at 
such eastern elongations as occur in March and April. When 
it is morning star, it is best seen in September and October. 

It is exceptional in the solar system in various ways. It is 
the nearest planet to the sun, receives the most light and heat, is 
the swiftest in its movement, and (excepting some of the aste- 
roids) has the most eccentric orbit, with the greatest inclination 
to the ecliptic. It is also the smallest in diameter (again ex- 
cepting the asteroids), and has the least mass of all the 
planets. 

317. Its Orbit. — Its mean distance from the sun is 36,000- 
000 miles, but the eccentricity of its orbit is so great (0.205) 
that the sun is 7,500000 miles out of the centre, and the radius 
vector ranges all the way from 28-J- millions to 43£, while the 
velocity in its orbit varies from 36 miles a second at perihe- 
lion to only 23 at aphelion. A given area upon its surface 
receives on the average nearly 7 times as much light and heat 
as it would on the earth; but the heat received at perihelion 



§ 317] THE PLANET'S MAGNITUDE, MASS, ETC. 221 

is greater than that at aphelion in the ratio of 9 : 4. For this 
reason there must be at least two seasons in its year due to 
the changing distance, even if the equator of the planet should 
be parallel to the plane of its orbit ; and if the planet's equa- 
tor is inclined nearly at the same angle as the Earth's, the 
seasons must be extremely complicated. 

The sidereal period is 88 days, and the synodic period, (or 
the time from conjunction to conjunction,) 116. The greatest 
elongation ranges from 18° to 28°, and occurs about 22 days 
before and after the inferior conjunction. The inclination of 
the orbit to the ecliptic is about 7°. 

318. The Planet's Magnitude, Mass, Etc. — The apparent 
diameter of Mercury ranges from 5" to about 13", according 
to its distance from us ; and the real diameter is very near 
3000 miles. This makes its surface about a seventh that of 
the earth, and its bulk or volume, one-eighteenth. The planet's 
mass is not accurately known ; it is very difficult to determine, 
since it has no satellite, and the values obtained from pertur- 
bations range very widely : it is probably between ^ and -fa 
of the mass of the earth. Its mass is, however, unquestion- 
ably smaller than that of any other planet, asteroids excepted. 
Our uncertainty as to its mass of course prevents us from 
assigning any certain values to its density, though probably it 
is not quite so dense as the earth. 

319. Telescopic Appearances, Phases, Etc. — As seen through 
the telescope, the planet looks like a little moon, showing 
phases precisely similar to those of our satellite. At inferior 
conjunction the dark side is towards us ; at superior conjunc- 
tion, the illuminated surface. At greatest elongation the 
planet appears as a half moon. It is gibbous between superior 
conjunction and greatest elongation, while between inferior 
conjunction and elongation it shows the crescent phase. 

Fig. 79 illustrates the phases of Mercury (and equally of Venus). 



222 MERCUKY. [§ 319 

The atmosphere of the planet cannot be as dense as that of 
Venus, because at a " transit " it shows no encircling ring of 
light, as Venus does (Art. 324) ; both Huggins and Vogel, 
however, report spectroscopic 1 observations which imply the 
presence of an atmosphere containing the vapor of water. 

Generally, the planet is so near the sun that it can be ob- 
served only by day, but when the proper precautions are 




Fig. 79. — Phases of Mercury and Venus. 

taken to screen the object-glass of the telescope from direct 
sunlight, the observation is not specially difficult. The sur- 
face presents very little of interest. It is brighter at the edge 
than at the centre, but until recently no markings have been 
observed well enough denned to give us any trustworthy in- 
formation as to its geography or even its rotation. 

Schroter, a German astronomer, the contemporary of the elder 
Herschel, and, to speak mildly, an imaginative man, early in the cen- 
tury reported certain observations which would seem to indicate the 
existence of high mountains upon the planet, and he deduced from 
his observations a rotation period of 24 hours, 5 minutes. Later ob- 
servers, with instruments certainly far more perfect, have not been 
able to verify his results, and they are now considered as of little 
weight. 

1 The planet's spectrum, in addition to the ordinary dark lines belong- 
ing to the spectrum of reflected sunlight, shows certain bands known to 
be due to water vapor, but it is not yet quite certain whether the vapor is 
in the planet's atmosphere or in our own. 



§ 319] TRANSITS OF MERCURY. 223 

In 1889 the Italian astronomer, Schiaparelli, announced 
that he had discovered certain permanent markings upon 
the surface of Mercury, and that from them he had ascer- 
tained that the planet rotates on its axis only once during its 
orbital period of 88 days ; i.e., it keeps the same face always 
turned towards the sun, behaving in this respect just as the 
moon does towards the earth. Owing, however, to the great 
eccentricity of its orbit, the planet has a large "libration" 
(Art. 155), amounting to nearly 23^-° on each side of the 
mean position ; i.e., seen from a favorable position on the 
planet's surface, the sun, instead of rising and setting daily 
as with us, would appear to oscillate back and forth in the 
sky to the extent of 47° every 88 days. 

This important discovery waited long for verification, the 
necessary observations being extremely difficult, but in 1896 
Mr. Lowell reported that his observations at Flagstaff fur- 
nish a complete confirmation of Schiaparelli's result. 

The " albedo" or reflecting power, of the planet is very low, 
only 0.13 ; somewhat inferior to that of the moon, and very 
much below that of any other of the planets. In the propor- 
tion of light given out at its different phases, it behaves like 
the moon, flashing out strongly near the full. 

No satellite is known, and there is no reason to suppose that 
it has any. 

320. Transits of Mercury. — At the time of inferior con- 
junction, the planet usually passes north or south of the sun, 
the inclination of its orbit being 7° ; but if the conjunction 
occurs when the planet is very near its node, it crosses the 
disc of the sun, and becomes visible upon it as a small, black 
spot, — not, however, large enough to be seen without a tele- 
scope, like Venus under similar circumstances. Since the 
earth passes the planet's node on May 7th and Nov. 9th, tran- 
sits can occur only near those dates. 

If the planet's orbit were truly circular, the conditions of transit 
would be the same at each node ; but at the May transits, the planet 



224 VENUS. [§ 320 

is near its aphelion, and, as a consequence, they are only about half 
as numerous as the others. For the November transits, the interval 
is usually 7 or 13 years ; for the May transits, 13 or 46. 22 synodic 
periods of Mercury are pretty nearly equal to 7 years ; 41 still more 
nearly equal to 13 years ; and 145 are almost exactly equal to 46 years. 
Hence, 46 years after a given transit another one at the same node is 
almost certain. During the first half of the twentieth century transits 
will occur as follows : — 

May 7th, 1924, and May 10th, 1937 ; Nov. 12th, 1907*; Nov. 6th, 
1914* ; Nov. 8th, 1927; and Nov. 12th, 1940. Only the two marked 
with an asterisk will be (partially) visible in the United States. 

Transits of Mercury are of no particular astronomical importance, 
except as furnishing accurate determinations of the planet's place. 

VENUS. 

321. The next planet in the order from the sun is Venus, 
the brightest and most conspicuous of all. It is so brilliant 
that at times it casts a distinct shadow, and is easily seen by 
the naked eye in the daytime. Like Mercury, the Greeks 
had two names for it, — Phosphorus as morning star, and 
Hesperus as evening star. 

Its mean distance from the sun is 67,200000 miles, and its 
distance from the earth ranges from 26,000000 miles (93 — 67) 
to 160,000000 (93+67). No other body ever comes so near 
the earth, except the moon and occasionally a comet. The 
eccentricity of its orbit is the smallest in the planetary system 
(only 0.007), so that the greatest and least distances of the 
planet from the sun differ from the mean only 470,000 miles. 
Its orbital velocity is about 22 miles per second. Its sidereal 
period is 225 days, or 7£ months ; and its synodic period, 584 
days, — a year and 7 months. From superior conjunction to 
elongation on either side is 220 days, while from inferior con- 
junction to elongation is only 71 or 72 days. The greatest 
elongation is 47° or 48°. The inclination of its orbit is about 3£°. 

322. Magnitude, Mass, Density, Etc. — The apparent diam- 
eter of the planet ranges from 67", at the time of inferior 



322] 



TELESCOPIC APPEARANCE, ETC. 



225 



conjunction, to only 11" at superior, the great difference de- 
pending upon the enormous variation in the distance of the 
planet from the earth. The real diameter of the planet in 
miles is about 7700. Its surface, compared with that of the 
earth, is T %^ ; its volume, -fij\. By means of the perturbations 
she produces upon the earth, the mass of Venus is found to be 
a little less than four-fifths of the earth's mass. Hence her 
density is about 86 per cent, and her superficial gravity 83 per 
cent of the earth's. A man who weighs 160 pounds here 
would weigh only about 133 pounds on Venus. 




Fig. 80. — Telescopic Appearances of Venus. 



323. General Telescopic Appearance, Phases, Etc. — The tele- 
scopic appearance of Venus is striking on account of her great 
brilliance, but exceedingly unsatisfactory because nothing is 
distinctly outlined upon the disc. When about midway be- 
tween greatest elongation and inferior conjunction the planet 
has an apparent diameter of 40", so that with a magnifying 



226 VENUS. §323] 

power of only 45 she looks exactly like the moon four days 
old, and of the same apparent size. (Very few persons, how- 
ever, would think so on the first view througli the telescope : 
the novice always underrates the apparent size of a telescopic 
object.) 

The phases of Venus were first discovered by Galileo in 1610, and 
afforded important evidence as to the truth of the Copernican System 
as against the Ptolemaic. 

Fig. 80 represents the planet's disc as seen at five points in its 
orbit. 1, 3, and 5 are taken at superior conjunction, greatest elonga- 
tion, and near inferior conjunction, respectively ; while 2 and 4 are at 
intermediate points. (No. 2 is badly engraved, however ; the sharp 
corners are impossible.) 

The planet attains its maximum brightness when its appar- 
ent area is at a maximum, about 36 days before and after 
inferior conjunction. 

According to Zollner, the albedo of the planet is 0.50; i.e., 
about three times that of the moon, and almost four times that 
of Mercury. It is, however, slightly exceeded by the reflect- 
ing power of Uranus and Jupiter, while that of Saturn is about 
the same. This high reflecting power has generally been con- 
sidered to indicate a surface mostly covered with clouds 
(though Lowell dissents from this, see Art. 325). The disc 
of Venus is brightest at the edge, as is also the case with 
Mercury, Mars, and the moon. 

324. Atmosphere of the Planet. — When the planet is near 
the inferior conjunction, the horns of the crescent extend 
notably beyond the diameter ; and when very near it a thin 
line of light has been seen by several observers to complete 
the whole circumference of the disc. This is due to the re- 
fraction of sunlight bent around the globe by the planet's 
atmosphere, a phenomenon still better seen when the planet is 
entering upon the sun's disc at a transit : the black disc is 
then encircled by a beautiful ring of light (see Fig. 138, A]> 



324] SURFACE-MARKINGS, ROTATION, ETC. 227 

pendix). From observations of the transit of 1874, Watson 
concluded that the planet's atmosphere must have a depth of 
about 55 miles (that of the earth being usually reckoned at 40 
miles). It is probably from one and a half to two times as 
dense as our own, and the spectroscope shows evidence of the 
presence of aqueous vapor in it. 

Many observers have also reported faint lights as visible at 
times on the dark portions of the planet's disc. These cannot 
be accounted for by any reflection or refraction of sunlight, 
but must originate on the planet's surface. They recall the 
Aurora Borealis and other electrical manifestations on the 
earth. 

325. Surface-Markings, Rotation, Etc. — As has been said, 
Venus is a very unsatisfactory telescopic object. She presents 
no obvious surface-markings, — nothing to most observers 
but occasional indefinite shadings : sometimes, however, when 
in the crescent phase, intensely bright spots have been re- 
ported near the " cusps," or points, of the crescent. These 
may perhaps be " ice-caps," like those which are seen on 
Mars. The darkish shadings may possibly be continents and 
oceans, dimly visible, or they may be atmospheric objects ; 
observations do not yet decide. From certain irregularities 
occasionally observed upon the " terminator," some have 
maintained that there are high mountains on the surface, 
but the evidence is by no means satisfactory. 

Lowell, in opposition to all previous observers, reports the dis- 
covery, at Flagstaff in 1896, of a system of permanent markings 
consisting of rather narrow, nearly straight, dark streaks, radiating 
like spokes from a sort of central " hub." He describes them as 
fairly definite in outline, but dim, as if seen through a luminous 
though unclouded atmosphere of considerable depth ; and he goes so 
far as to give a map of the planet, with names attached to some of 
the leading features. It remains to be seen whether his observations 
will be confirmed. 

No satellite has ever been discovered; not, however, for 
want of earnest searching. Venus probably has none. 



228 ROTATION OF THE PLANET. §325] 

325*. Rotation of the Planet. — Schroter, early in the cen- 
tury, assigned a rotation period of 23h. 21m., and the result 
was partially confirmed by some later observers, and generally 
accepted until recently, though not without misgivings. The 
planet's disc shows no sensible oblateness, as it ought to do if 
his figures were correct. The observations of Schiaparelli, on 
the other hand, while he did not consider them absolutely 
conclusive, indicate a very slow rotation, probably of 225 
days, identical with the planet's orbital period, as in the case 
of Mercury and the moon. Mr. Lowell considers that his 
observations absolutely prove the correctness of this conclu- 
sion, and also that the equator of Venus is only very slightly 
inclined to her orbit. 

326. Transits. — Occasionally Venus passes between the 
earth and the sun at inferior conjunction, giving us a so-called 
"transit." She is then visible even to the naked eye as a 
black spot on the disc, crossing it from east to west. When 
the transit is central, it occupies about eight hours, but when 
the track lies near the edge of the disc, the duration is of 
course correspondingly shortened. Since the sun passes the 
nodes of the orbit on June 5th and December 7th, all transits 
must occur near these dates, but they are very rare phenomena. 

Their special interest consists in their availability for the 
purpose of finding the sun's parallax (see Appendix, Arts. 516- 
519). The first observed transit (in 1639) was seen by only 
two persons, — Horrox and Crabtree, in England, but the four 
which have occurred since then have been extensively observed 
in all parts of the world where they were visible, by scientific 
expeditions sent out for the purpose by the different govern- 
ments. The transits of 1769 and 1882 were visible in the 
United States. 

327. Recurrence and Dates of Transits. — Five synodic, or thir- 
teen sidereal revolutions of Venus are very nearly equal to eight years, 
the difference being little more than one day; and still more nearly-^ 




§328] MAns . 229 

in fact, almost exactly — !2 1 -5 wars are equal to 
152 synodic, or 395 sidereal revolutions* If, 
then, we have a transit at any time, we may 
have another at the same node eight years earlier 
or later. Sixteen years before or after, it will 
be impossible, and no other transit can occur 
at the same node until after the lapse of 285 
or 243 years, although a transit or pair of tran- 
Pig. gl. sits may oceni- at the other node in about half 

Transit of Venub Tracks, that time. Transits of Venus have occurred, or 
w ill occur at the following dates : — 

j Dec. 7th, 1631. (June 5th, 1761. 

( Dec. 4th, 1639. < June 3d, 17(50. 

< Dec. 0th, 1874. * (June 8th, 2001. 

I Dec. 6th, 1882. ( June 6th, 2012. 

Fig. 81 shows the tracks of Venus across the sun's disc in the 
transits of 1874 and 1882. 

MAKS. 

328. This planet is also prehistoric as to its discovery. It 
is so conspicuous in color and brightness, and in the extent 
and apparent capriciousness of its movement among the stars, 
that it could not have escaped the notice; of the very earliest 
observers. 

Its mean distance from the sun is a little more than one and 
a half times that of* the earth (141,500000 miles), and the 
eccentricity of its orbit is so considerable (0.093) that Its 
radius vector varies more than 20,000000 miles. At opposi- 
tion the planet's average distance from the earth is 48,000000 
miles. When opposition occurs near the planet's perihelion, 
this distance is reduced to 35,500000 miles, while near aphelion 
it is over 01,000000. At superior conjunction, the average 
distance from the earth is 234,000000. 

The apparent diameter and brilliancy of the planet of course 
vary enormously with those great changes of distance. At a 
"favorable" opposition (when the distance is at its minimum), 



230 MAKS. [§ 329 

the planet is more than fifty times as bright as at superior 
conjunction, and fairly rivals Jupiter; when most remote, it 
is hardly as bright as the Pole-star. 

The favorable oppositions occur always in the latter part of 
August (at which time the earth as seen from the sun passes the 
perihelion of the planet), and at intervals of 15 or 17 years. The last 
such opposition was in 1892. 

The inclination of the orbit is small, 1° 51'. 

The planet's sidereal period is 687 days, or 1 year 10| 
months ; its synodic period is much the longest in the plane- 
tary system, being 780 days, or nearly 2 years and 2 months. 
During 710 of the 780 days it moves eastward, and retro- 
grades during 70. 

329. Magnitude, Mass, Etc. — The apparent diameter of the 
planet ranges from 3".6 at conjunction to 24".5 at a favorable 
opposition. Its real diameter is very closely 4230 miles, with 
an error of perhaps 20 miles one way or the other. This makes 
its surface about two-sevenths, and its volume one-seventh of 
the earth's. 

Its mass is a little less than i of the earth's mass. This 
makes its density 0.73 and superficial gravity 0.38; a body 
which here weighs 100 pounds would have a weight of only 
38 pounds on the surface of Mars. 

330. General Telescopic Aspect, Phases, Albedo, Atmosphere, 
Etc. — When the planet is nearest the earth, it is more favor- 
ably situated 1 for telescopic observation than any other 
heavenly body, — the moon alone excepted. It then shows a 
ruddy disc which, with a power of 75, is as large as the moon. 

1 Venus at times conies nearer; but when nearest she is visible only by 
daylight, and the hemisphere presented to the earth is mostly dark. 




§ 331] TELESCOPIC ASPECT. 231 

Since its orbit is outside the earth's, it never exhibits the 
crescent phases like Mercury and Venus ; but at quadrature it 
appears distinctly gibbous, as in Fig. 82, 
about like the moon three days from the 
full. Like Mercury, Venus, and the moon, 
its disc is brighter at the limb (i.e., at the 
circular edge) than at the centre ; but at 
the "terminator," or boundary between 
day and night upon the planet's surface, 
there is a slight shading which, taken in 
connection with certain other phenomena, 
indicates the presence of an atmosphere. 

Mars at Quadrature. . 

This atmosphere, however, contrary to 
opinions formerly held, is probably much less dense than that 
of the earth, the low density being indicated by the infre- 
quency of clouds and of other atmospheric phenomena famil- 
iar to us upon the earth, to say nothing of the fact that since 
the planet's superficial gravity is less than § the force of 
gravity on the earth, a dense atmosphere would be impossible. 

More than twenty years ago Huggins, Janssen, and Vogel 
all reported the lines of water-vapor in the spectrum of the 
planet's atmosphere ; but the observations of Campbell, at the 
Lick Observatory in 1894, throw great doubt on their result, 
and show that the water-vapor, if present at all, is too small 
in amount to give decisive evidence of its presence. 

Zollner gives the albedo of Mars as 0.26, just double that of 
Mercury, and much higher than that of the moon, but only 
about half that of Venus and the major planets. Near oppo- 
sition, the brightness of the planet suddenly increases, in the 
same way as that of the moon near the full (Art. 162). 

331. Rotation, Etc. — The spots upon the planet's disc en- 
able us to determine its period of rotation with great precision. 



232 SURFACE AND TOPOGRAPHY. [§ 331 

Its sidereal day is found to be 24 hours, 37 minutes, 22.67 
seconds, with a probable error not to exceed one-fiftieth of a 
second. This very exact determination is effected by compar- 
ing drawings of the planet made by Huyghens and Hooke 
more than 200 years ago with others made recently. 

The inclination of the planet's equator to the plane of its 
orbit is very nearly 24° 50' (26° 21' to the ecliptic). So far, 
therefore, as depends upon that circumstance, Mars should 
have seasons substantially the same as our own, and certain 
phenomena of the planet's surface, soon to be described, make 
it evident that such is the case. 

The planet's rotation causes a slight but sensible flattening at 
the poles, — about ^J-^, according to the latest determinations. 

(Much larger values, now known to be certainly erroneous, are 
found in the older text-books.) 

332. Surface and Topography. — With even a small tele- 
scope, not more than three or four inches in diameter, the 
planet is a very beautiful object, showing a surface diversified 
with markings dark and light, which for the most part are 
found to be permanent objects. Occasionally, however, for a 
few hours at a time, we see others of a temporary character, 
supposed to be clouds; but these are srirprisingly rare as com- 
pared with clouds upon the earth. The permanent markings 
on the planet are broadly divisible into three classes, — 

First, The white patches, two of which are specially conspicu- 
ous near the planet's poles, and are by many supposed to be 
masses of snow or ice, since they behave just as would be 
expected if such were the case. The northern one dwindles 
away during the northern summer, when the North Pole is 
turned towards the sun, while the southern one grows rapidly 
larger ; and vice versa during the southern summer. But the 
probable low temperature of the planet (Art. 335) makes it at 
least doubtful whether the apparent " snow and ice " is really 
congealed water, or some quite different substance. 



§ 332] MARS. 233 

Second, Patches of bluish-gray or greenish shade, covering 
about | of the planet's surface, until recently generally sup- 
posed to be bodies of water, and therefore called " seas " and 
"oceans/' But more recent observations show a great variety 
of details within these areas, and such changes of appearance 
following the seasons of the planet, that this theory is no 
longer tenable, and they seem more likely to be regions cov- 
ered with something like vegetation. 

Third, Extensive regions of various shades of orange and 
yellow, covering nearly five-eighths of the surface, and inter- 
preted as land. These markings are, of course, best seen when 
near the centre of the planet's disc ; near the limb they are 
lost in the brilliant light which there prevails, and at the 
terminator they fade out in the shade. 




Fig. 83.— Telescopic Views of Mars. 

Fig. 83 gives an idea of the planet's general appearance, though 
without pretending to minute accuracy. 

333. Recent Discoveries. The Canals and their Gemination.— 

In addition to these three classes of markings, the Italian 
astronomer Schiaparelli in 1877 and 1879 reported the dis- 
covery of a great number of fine straight lines, or "canals" 
as he called them, crossing the ruddy portions of the planet's 
disc in all directions ; and in 1881 he announced that some of 
them become double at times. These new markings are faint, 
and very difficult to see, and for several years there was a 
strong suspicion that he was misled by some illusion ; more 
recently, however, his results have been abundantly confirmed, 



234 



SURFACE AND TOPOGRAPHY. 



[§ 333 



both, in Europe and in the United States. It appears that in 
the observation of these objects the power of the telescope is 
less important than steadiness of the air and keenness of the 
observer's vision. Nor are they usually best seen when Mars 
is nearest, but their visibility depends largely upon the season 
on the planet ; and this is especially the case with their "gem- 




FiG. 83*. 

ination." Fig. 83* from one of Mr. Lowell's drawings in 
1894, gives an idea of the extent and complexity of the canal- 
system ; but the reader must not suppose that in the telescope 
it stands out with any such conspicuousness. The figure 
shows also how some of the canals cross the so-called " seas/' 
and disprove the propriety of the name. 



333*. As to the real nature and office of the " canals " there is a 
wide difference of opinion, and it is very doubtful if their true ex- 
planation has yet been reached. Indeed it is still quite possible that 
some of the peculiar phenomena reported are illusions, based on 
what the observers think they ought to see : it is easy to be deceived 
in attempting to interpret intelligibly what is barely visible. Ac- 
cording to Flammarion, Lowell, and other zealous observers of the 
planet, the polar caps are really snow-sheets, which melt in the 
(Martian) spring, and send the water towards the planet's equator 



§ 333*] MAPS OF THE PLANET. 235 

over its nearly level plains (for no high mountains have yet been 
discovered there), obscuring for several weeks the well-known mark- 
ings which are visible at other times. In Lowell's view the dark 
regions on the planet's surface are areas covered with some sort of 
vegetation, while the ruddy portions are barren deserts, intersected 
by the canals, which he believes to be really irrigating water courses ; 
and on account of their straight ness, and some other characteristics, 
he is disposed to regard them as artificial. When the water reaches 
these " canals " vegetation springs up along their banks, and these 
belts of verdure are what we see with our telescopes, — not the narrow 
water-channels themselves. Where the canals cross each other and 
the water supply is more abundant, there are dark, round " lakes," as 
they have been called, which he interprets as " oases." All of this 
theoretical explanation rests, however, upon the assumption that the 
planet's temperature is high enough to permit the existence of water 
in the liquid state ; to say nothing of other difficulties. But what- 
ever may be the explanation, there is no longer any doubt as to the 
existence of the " canals," nor that they (and other features of the 
surface) undergo real changes with the progress of the planet's sea- 
sons. Their " gemination," however, still remains a mystery, and in 
the report of the Harvard College Observatory for 1896 it is stated 
that some experiments recently made there throw a good deal of 
doubt on the " objective reality " of the doubling. 

334. Maps of the Planet. — A number of maps of Mars have 
been constructed by different observers since the first was made by 
Maedler in 1830. Fig. 84 is reduced from one published in 1888 by 
Schiaparelli, and shows most of his " canals " and their " gemination." 
While there may be some doubt as to the accuracy of the minor de- 
tails, there can be no question that the main features of the planet's 
surface are substantially correct. The nomenclature, however, is in a 
very unsettled condition. Schiaparelli has taken his names mostly 
from ancient geography, while the English areographers, 1 following 
the analogy of the lunar maps, have mainly used the names of astrono- 
mers who have contributed to our knowledge of the planet's surface. 

1 The Greek name of Mars is Ares, hence " Areography " is the descrip- 
tion of the surface of Mars. 



236 



MARS. 



[§334 




o 



§ 336] SATELLITES. 237 

335. Temperature. — As to the temperature of Mars we 
have no certain knowledge at present. Unless the planet 
has some unexplained sources of heat it ought to be very cold. 
Its distance from the sun reduces the intensity of solar radi- 
ation upon its surface to less than half its value upon the 
earth, and its atmosphere cannot well be as dense as at the 
tops of our loftiest mountains. On the other hand things look 
very much as if liquid water and vegetable life were present 
there. It is earnestly to be hoped that before long we may 
come into possession of some heat-measuring apparatus suffi- 
ciently delicate to decide whether the planet's surface is 
really intensely cold or reasonably warm, — for of course 
there are various conceivable hypotheses which might account 
for a high temperature at the surface of Mars. 

336. Satellites. — The planet has two satellites, discovered 
by Hall, at Washington, in 1877. They are extremely small, 
and observable only with very large telescopes. The outer one, 
Deimos, is at a distance of 14,600 miles from the planet's 
centre, and has a sidereal period of 30 hours, 18 minutes ; 
while the inner one, Phobos, is at a distance of only 5800 
miles, and its period is only 7 hours, 39 minutes, — less than 
one-third of the planet's day. (This is the only case known 
of a satellite with a period shorter than the revolution of its 
primary.) Owing to this fact, it rises in the west, as seen from 
the planet's surface, and sets in the east, completing its strange 
backward diurnal revolution in about 11 hours. Deimos, on 
the other hand, rises in the east, but takes nearly 132 hours 
in its diurnal circuit, which is more than four of its months. 
Both the orbits are sensibly circular, and lie very closely in 
the plane of the planet's equator. 

Micrometric measures of the diameter of such small objects are im- 
possible, but from photometric observations, Prof. E. C. Pickering, 
assuming that they have the same reflecting power as that of Mars 
itself, estimates the diameter of Phobos as about seven miles, and 



238 HABITABILITY OF MARS. [§336 

that of Deimos as five or six. Mr. Lowell, however, from his obser- 
vations of 1894, deduces considerably larger values, viz. 10 miles for 
Deimos, and 36 for Phobos. If this is correct, Phobos, seen in the 
zenith from the point on the planet's surface directly beneath him, 
would appear somewhat larger than the moon but only about half as 
bright. Deimos would be no brighter than Venus. 

337. Habitability of Mars. — As to this question we can only 
say that, different as must be the conditions on Mars from those pre- 
vailing on the earth, they differ less from ours than those on any 
other heavenly body observable with our present telescopes ; and if 
life, such as we know it upon the earth, can exist on any of the 
planets, Mars is the one. If we could waive the question of temper- 
ature^ and assume, with Flammarion and others, that the polar caps 
consist of frozen water, then it would become extremely probable 
that the growth of vegetation is the explanation of many of the 
phenomena actually observed. 

Mr. Lowell goes further and argues the presence of intelligent 
beings, possessed of high engineering skill, from the apparent " ac- 
curacy " with which the " canals" seem to be laid out, in a well 
planned system of irrigation. But at present, and until the temper- 
ature problem is solved, such speculations appear rather premature, 
to say the least. 

THE ASTEROIDS, OR MINOR PLANETS. 

338. The asteroids x are a multitude of small planets circling 
around the sun in the space between Mars and Jupiter. It 
was early noticed that between Mars and Jupiter there is a 
gap in the series of planetary distances, and when Bode's Law 
(Art. 284) was published in 1772, the impression became very 
strong that there must be a missing planet in the space, — an 
impression greatly strengthened when Uranus was discovered 
in 1781, at a distance precisely corresponding to that law. An 
association was formed to search for the missing planet, but 
rather strangely the first discovery was made, not by a mem- 

1 They were first called "asteroids" (i.e., "star-like" bodies) by Sir 
William Herschel early in the century, because, though really planets, 
the telescope shows them only as stars, without a sensible disc. 



§ 338] THE ASTEROIDS. 239 

ber of the organization, but by the Sicilian astronomer, Piazzi, 
who on the very first night of the present century (Jan. 1st. 
1801) discovered a planet which he named Ceres, after the 
tutelary divinity of Sicily. The next year Pallas was discov- 
ered by Olbers. Juno was found in 1801 by Harding, and in 
1807 Olbers, who had broached the theory of an exploded 
planet, discovered the fourth, Vesta, the only one which is 
bright enough ever to be easily seen by the naked eye. The 
search was kept up for some years longer, but without suc- 
cess, because the searchers did not look for small enough 
objects. The fifth asteroid (Astraea) was found in 1815 by 
Hencke, an amateur who had resumed the subject afresh by 
studying the smaller stars. In 1817 three more were discov- 
ered, and every year since then has added from one to twenty. 
On Jan. 1st, 1897, the list included nearly 450. Of late the 
number known has increased with great rapidity ; since 1892 
more than 150 have been discovered, all but seven by means 
of photography, which in that year was first employed for the 
purpose by Max Wolf of Heidelberg. Nearly all the recent 
discoveries are due to him, and to Charlois of Nice ; especially 
to the latter, who is already responsible for over 100. Nearly 
all have names, but more generally they are designated by 
numbers in the order of their discovery. Thus, Ceres is ©, 
Thule is (279), etc. 

339. Their Orbits. — The mean distances of the different 
asteroids from the sun differ considerably, and the periods, of 
course, correspond. Medusa, (149), and Brucia, (323), are nearest 
to the sun of those at present known, their distance from the 
sun being about 200,000000 miles, and their periods about 3 
years and 50 days. Thule, (279), is the most remote, with a 
mean distance of 4.30 (400,000000 of miles), and a period 
only a month less than 9 years. 

The inclinations of the orbits to the ecliptic average nearly 
8°. The orbit of Pallas, @, is inclined at an angle of 35°, and 
seven others exceed 25°. The eccentricity of the orbits is very 



240 THE BODIES THEMSELVES. [§ 339 

large in many cases. Aethra, (132), has the almost cometary 
eccentricity of 0.38, and ten others have an eccentricity ex- 
ceeding 0.30. 

340. The Bodies Themselves. — The four first discovered, 
and one or two others, when examined with a powerful tele- 
scope, show a perceptible disc, not large enough, however, for 
satisfactory measurement. Vesta is much the brightest of 
them, and until very recently was therefore supposed to be 
the largest. In 1894-5 Mr. Barnard, however, at the Lick 
Observatory, succeeded in making a set of micrometric meas- 
ures which gave the following rather surprising results. He 
finds the diameter of Ceres to be 485 miles ; of Pallas, 304 ; of 
Vesta, 243 ; and of Juno only 118. But the " probable error " 
must be considerable. The albedo of Vesta must much ex- 
ceed that of the others. None of these bodies except the first 
four can be more than about 50 or 60 miles in diameter ; and 
the newly discovered ones, barely visible in a 12-inch tele- 
scope, cannot be larger than the moons of Mars, perhaps 
10 or 20 miles in diameter. 

As to the individual masses and densities, we have no 
certain knowledge. 

If the density of Ceres is about the same as that of the rocks which 
compose the earth's crust, her mass may be as great as T oVo tnat °^ 
the earth. If so, gravity on her surface would be about ^ of gravity 
here, so that a body would fall about eight inches in the first second. 
Of course on the smaller asteroids it would be much less. If the 
hypothetical inhabitant and owner of one of these little planets 
should throw a stone, it would become independent, circling around 
the sun in an orbit of its own, and never returning to the planet. 

It is, however, possible from the perturbations they produce 
on Mars to estimate a limit for the aggregate mass of the 
whole swarm. According to Leverrier, it cannot exceed one- 
fourth the mass of the earth, but may be very much less. A 
still more recent computation by Eavene in 1896 indicates a 
total mass about T {^ that of the earth. 



§ 340] THE ASTEROIDS. 241 

The united mass of those at present known would make only a 
small fraction of such a body, — hardly a thousandth of it ; presum- 
ably, therefore, the number still undiscovered is to be counted by 
thousands, and they must be, for the most part, very much smaller 
than those already known. How long it will be considered worth 
while to hunt for new ones is a question now forcing itself on the 
attention of astronomers. 

341. Origin. — As to this we can only speculate. It is hardly 
possible to doubt, however, that this swarm of little rocks in 
some way represents a single planet of the terrestrial group. 
A commonly accepted view is that the material, which, accord- 
ing to the nebular hypothesis, once formed a ring (like one of 
the rings of Saturn), and ought to have collected to make a 
single planet, has failed to be so united; and the failure is 
ascribed to the perturbations produced by the giant Jupiter, 
whose powerful attraction is supposed to have torn the ring 
to pieces, and thus prevented the normal development of a 
planet. Another view is that the asteroids may be fragments 
of an exploded planet. If so, there must have been not one, 
aut many, explosions ; first of the original body, and then of 
the separate pieces, for it is demonstrable that no single explo- 
sion could account for the present tangle of orbits. 

342. Intra-Mercurial Planets. — It is not improbable that 
there is a considerable quantity of matter circulating around the sun 
inside the orbit of Mercury. This has been believed to be indicated 
by an otherwise unexplained advance of the perihelion of its orbit. 
It has been somewhat persistently supposed that this intra-Mercurial 
matter is concentrated into one, or possibly two, planets of consider- 
able size, and such a planet has several times been reported as dis- 
covered, and has even been named " Vulcan." We can only say 
here that the supposed discoveries have never been confirmed, and 
the careful observations of total solar eclipses during the past ten 
years make it practically certain that there is no " Vulcan." Perhaps, 
however, there is an intra-Mercurial family of " asteroids.'' But they 
must be very minute or some of them w r ould certainly have been 
found either during eclipses or crossing the sun's disc ; a planet as 
much as 200 miles in diameter could hardly have escaped discovery. 



242 THE ZODIACAL LIGHT. [§ 343 

343. The Zodiacal Light. — This is a faint beam of light 
extending from the sun both ways along the ecliptic. In the 
evening it is best seen in the months of February, March, and 
April, and in our latitudes then extends about 90° eastward 
from the sun ; in the tropics, it is said that it can be followed 
quite across the sky, forming a complete ring. At the point 
in the sky directly opposite to the sun, there is a patch of 
slightly greater luminosity, called the " Gegenschein" or 
" counter-glow." The region near the sun is fairly bright 
and even conspicuous, but the more distant portions are ex- 
tremely faint and can be observed, like the fainter portions 
of the milky way, only in places where there is no illumina- 
tion of the air by artificial lights. The spectrum is a simple, 
continuous spectrum, without markings of any hind. 

We emphasize this, because it has often been mistakenly reported 
that the line which characterizes the spectrum of the Aurora Borealis 
appears in the spectrum of the zodiacal light. 

The cause of the phenomenon is not certainly known. Some 
imagine that the zodiacal light is only an extension of the solar 
corona (whatever that may be), which is not perhaps unlikely; 
but on the whole the more prevalent opinion seems to be that 
it is due to sunlight, reflected from myriads of small meteoric 
bodies circling around the sun, nearly in the plane of the eclip- 
tic, thus forming a thin, flat sheet (something like one of 
Saturn's rings), which extends far beyond the orbit of the 
earth. Near the sun, within the orbits of Mercury and Venus, 
they are supposed to be much more numerous than at a greater 
distance ; thus accounting for the greater brightness of the 
zodiacal light in that part of the sky, notwithstanding the fact 
that all the meteoric particles within 90° from the sun would 
present to us less than half their illuminated surface : if 
globular, they would show a crescent phase like the moon 
between new and half. 

As for the " Gegenschein" this is explained by supposing 
that the particles opposite to the sun in the sky " flash out y 



§ 343] THE ZODIACAL LIGHT. 243 

in the same way the moon does at the full. See Art. 162. 

We have no direct evidence as to the size of the meteoric 
particles, though the analogy of shooting stars suggests that 
they are probably very small. See Art. 410. 

The peculiar disturbance of Mercury, referred to in the preceding 
article, may be, perhaps, due to the denser portion of this ring near 
the sun, and this is the reason why we consider the subject here in 
connection with the planets, rather than later in connection with the 
subject of meteors. The theory has also been maintained that the 
zodiacal light is due to a meteoric ring surrounding the earth. 



244 THE MAJOK PLANETS. [§344 



CHAPTER XII. 

THE MAJOR PLANETS. — JUPITER : ITS SATELLITE SYS- 
TEM ; THE EQUATION OF LIGHT, AND THE DISTANCE 

OF THE SUN. SATURN : ITS RINGS AND SATELLITES. 

URANUS : ITS DISCOVERY, PECULIARITIES, AND 

SATELLITES. NEPTUNE : ITS DISCOVERY, PECULIARI- 
TIES, AND SATELLITE. 

344. Jupiter, the nearest of the major planets, stands next 
to Venus in the order of brilliance among the heavenly bodies, 
being fully five or six times as bright as Sirius, the most bril- 
liant of the stars, and decidedly superior to Mars, even when 
Mars is nearest. It is not, like Venus, confined to the twilight 
sky, but at the time of opposition dominates the heavens all 
night long. 

Its orbit presents no marked peculiarities. The mean dis- 
tance of the planet from the sun is a little more than five astro- 
nomical units (483,000000 miles), and the eccentricity of the 
orbit is not quite ■£$, so that the actual distance ranges about 
21,000000 miles each side of the mean. At an average oppo- 
sition, the planet's distance from the earth is about 390,000000 
miles, while at conjunction it is distant about 580,000000 ; but 
it may come as near to us as 370,000000, and may recede to a 
distance of nearly 600,000000. 

The inclination of its orbit to the ecliptic is only 1° 19 f . Its 
sidereal period is 11.86 years, and the synodic is 399 days (a 
figure easily remembered), a little more than a year and a 
month. 

345. Dimensions, Mass, Density, Etc. — The planet's apparent 
diameter varies from 50" to 32", according to its distance from 



§345] GENERAL TELESCOPIC ASPECT, ETC. 245 

the earth. The disc, however, is distinctly oval, so that while 
the equatorial diameter is 88,200 miles, the polar diameter is 

only 83,000. The mean diameter, ( a ~*~ j (see Art. 95), is 

86,500 miles, or very nearly eleven times that of the earth. 

Its surface, therefore, is 119, and its volume or bulk 1300 
times that of the earth. It is by far the largest of all the 
planets, — larger, in fact, than all the rest united. 

Its mass is very accurately known, both by means of its 
satellites and from the perturbations it produces upon certain 
asteroids. It is 10 1 48 of the sun's mass, or about 316 times that 
of the earth. 

Comparing this with its volume, we find its mean density to 
be 0.24; i.e., less than one-fourth the density of the earth, 
and almost precisely the same as that of the sun. Its surface 
gravity is about 2f times that of the earth, but varies nearly 
20 per cent between the equator and poles of the planet on 
account of its rapid rotation. 

346. General Telescopic Aspect, Albedo, Etc. — In even a 
small telescope the planet is a fine object, for a magnifying 
power of only 60 makes its apparent diameter, even when 
remotest, equal to that of the moon. With a large instrument 
and a magnifying power of 200 or 300, the disc is covered with 
an infinite variety of detail, interesting in outline and rich in 
color, changing continually as the planet turns on its axis. 
For the most part the markings are arranged in " belts " par- 
allel to the planet's equator, as shown in Fig. 85. 

The left-hand one of the two larger figures is from a drawing by 
Trouvelot (1870), and the other from one by Vogel (1880). The 
smaller figure below represents the planet's ordinary appearance in 
a three-inch telescope. 

Near the limb the light is less brilliant than in the centre of 
the disc, and the belts there fade out. The planet shows no 
perceptible phases, but the edge which is turned away from 



246 



JUPITER. 



[§346 



the sun is usually sensibly darker than the other. According 
to Zollner, the mean albedo of the planet is 0.62, which is ex- 
tremely high, that of white paper being 0.78. The question 
has been raised whether Jupiter is not to some extent self- 
luminous, but there is no proof and little probability that such 
is the case. 




Fig. 85. — Telescopic Views of Jupiter. 

347. Atmosphere and Spectrum. — The planet's atmosphere 
must be very extensive. The forms visible with the telescope 
are nearly all evidently atmospheric. In fact, the low mean 
density of the planet makes it very doubtful whether there is 
anything solid about it anywhere, — whether it is anything 
more than a ball of fluid overlaid by cloud and vapor. 

The spectrum of the planet differs less from that of mere re- 
flected sunlight than might have been expected, showing that 
the light is not obliged to penetrate the atmosphere to any 



§347] ROTATION. 247 

great depth before it encounters the reflecting envelope of 
clouds. There are, however, dark shadings in the red and 
orange parts of the spectrum that are probably due to the 
planet's atmosphere, and seem to be identical in position with 
certain bands which are intense in the spectra of Uranus and 
Neptune. 

348. Rotation. — Jupiter rotates on its axis more swiftly 
than any other of the planets. Its sidereal day has a length 
of about 9 hours, 55 minutes. The time can be given only ap- 
proximately, not because it is difficult to find and observe well- 
defined objects on the disc, but because different results are 
obtained from different spots, according to their nature and 
their distance from the equator, — the differences amounting 
to six or seven minutes. Speaking generally, spots near the 
equator indicate a shorter period of rotation than those near 
the poles, just as is the case with the sun. 

In consequence of the swift rotation, the planet's " oblate- 
ness " or " polar compression " is quite noticeable, — about -fa. 
The plane of rotation nearly coincides with that of the orbit, 
the inclination being only 3°, so that there can be no well- 
marked seasons on the planet due to the causes which produce 
our own seasons. 

349. Physical Condition. — This is obviously very different 
from that of the earth or Mars. No permanent markings are 
found upon the disc, though occasionally some which may be 
called "sub-permanent" do appear, as, for instance, the "great 
red spot " shown in Fig. 85. This was first noticed in 1878, 
became extremely conspicuous for several years, and until 
1896 remained visible as a faded ghost of itself. Were it 
not that during the 18 years of its visibility it has changed 
the length of its apparent rotation by about six seconds (from 9 
hours, 55 minutes, 34.9 seconds to 9 hours, 55 minutes, 40.2 
seconds), we might suppose it permanently attached to the 



248 JUPITER. [§349 

planet's surface, and evidence of a coherent mass underneath. 
As it is, opinion is divided on this point. 

Many things in the planet's appearance indicate a high 
temperature, as, for instance, the abundance of clouds, and 
the swiftness of their transformations ; and since on Jupiter 
the solar light and heat are only -^ Y as intense as here, we are 
forced to conclude that it gets very little of its heat from 
the sun, but is probably hot on its own account, and for the 
same reason that the sun is hot ; viz,, as the result of a process 
of condensation. In short, it appears very probable, as has 
been intimated before, that the planet is a sort of " semi-sun" 
— hot, though not so hot as to be sensibly self-luminous. 

350. Satellites. — Jupiter has five satellites. Four of them 
are so large as to be seen easily with a common opera glass : 
the fifth, discovered by Barnard at the Lick Observatory in 
1892, is, on the other hand, extremely small, and visible only 
in the most powerful instruments. The four large satellites 
were in a sense the first heavenly bodies ever " discovered" 
having been found by Galileo in January, 1610, with his 
newly invented telescope. 

The old satellites are still usually known as the first, second, 
etc., in the order of their distance from the planet. The dis- 
tances range from 262,000 to 1,169,000 miles, and their side- 
real periods from 42 hours to 16f days. Their orbits are 
sensibly circular, and lie very nearly in the plane of the 
equator. The third satellite is much the largest, having a 
diameter of about 3600 miles, while the others are betweei) 
2000 and 3000. 

For some reason, the fourth satellite is a very dark-complexione<l 
body, so that when it crosses the planet's disc it looks like a black 
spot hardly distinguishable from its own shadow, while the others, 
under similar circumstances, appear bright, dark, or invisible, accord- 
ing to the brightness of the part of the planet which happens to form 
the background. With very powerful instruments spots are some- 



§ 350] SATELLITE PHENOMENA. 249 

times visible on their surfaces, and there are unexplained variations 
in their brightness ; some observers also have reported irregularities 
in their forms, as if they were not solid. In the case of the fourth 
satellite, a certain regularity in the changes indicates that it follows 
the example of our moon in always keeping the same face towards 
the planet. 1 

351. Eclipses and Transits. — The orbits of the satellites are 
so nearly in the plane of the planet's orbit that with the ex- 
ception of the fourth, which sometimes escapes, they are 
eclipsed at every revolution, and also cross the planet's disc 
at every conjunction. When the planet is either at opposition 
or conjunction, the shadow, of course, is directly behind it, and 
we cannot see the eclipse at all. At other times we ordinarily 
see only the beginning or the end ; but when the planet is at 
or near quadrature the shadow projects so far to one side that 
the whole eclipse of every satellite, except the first, takes 
place clear of the disc. An eclipse is a gradual phenomenon, 
the satellite disappearing by becoming slowly fainter and 
fainter as it plunges into the shadow, and reappearing in the 
same leisurely way. 

Two important uses have been made of these eclipses : they 
have been employed for the determination of longitude, and 
they furnish the means of ascertaining the time required by 
light to traverse the space between the earth and the sun. 

352. The Equation of Light. — When we observe a celestial 
body we see it not as it is at the moment of observation, but 
as it teas at the moment when the light which we see left it. 
If we know its distance in astronomical units, and know how 
long light takes to traverse that unit, we can at once cor- 
rect our observation by simply dating it back to the time when 
the light started from the object. The necessary correction is 
called the " equation of light," and the time required by light to 
traverse the astronomical unit of distance is the "Constant 

1 See note at end of the chapter. 



250 



JUPITER. 



[§352 



of the Light-equation 

shall see). 



(not quite 500 seconds, as we 



It was in 1675 that Roemer. the Danish astronomer, (the inventor 
of the transit instrument, meridian-circle, and prime-vertical instru- 
ment, — a man almost a century in advance of his day,) found that 
the eclipses of Jupiter's satellites show a peculiar variation in their 
times of occurrence, which he explained as due to the time taken by 
light to pass through space. His bold and original suggestion was 
neglected for more than 50 years, until long after his death, when 
Bradley's discovery of aberration proved the correctness of his views. 

353. Eclipses of the satellites recur at intervals which are 
really almost exactly equal (the perturbations being very slight), 
and the interval can easily be determined and the times tab- 
ulated. But if we thus predict the times of the eclipses during 

a whole synodic period of 
the planet, then, beginning 
at the time of opposition, it 
is found that as the planet 
recedes from the earth, the 
eclipses, as observed, fall con- 
stantly more and more be- 
hindhand, and by precisely 
the same amount for all 
four satellites. The differ- 
ence between the predicted 
and observed time continues 
to increase until the planet 
is near conjunction, when 
the eclipses are almost 17 
minutes later than the pre- 
diction. After the conjunction they quicken their pace, and 
make up the loss, so that when opposition is reached once 
more they are again on time. 

It is easy to see from Fig. 86 that at opposition the planet 




Fig. 86. 
Determination of the Equation of Light. 



§ 353] THE EQUATION OF LIGHT. 251 

is nearer the earth, than at conjunction by just two astronom- 
ical units ; i.e., JB — JA = 2SA, and light coming from J to 
the earth when it is at A, will, therefore, make the journey 
quicker than when it is at B, by twice the time it takes light 
to pass from S to A. 

The whole apparent retardation of eclipses between opposi- 
tion and conjunction must therefore be exactly twice the time 1 
required for light to come from the sun to the earth. In this way 
the " light-equation constant " is found to be very nearly 499 
seconds, or 8 minutes, 19 seconds, with a probable error of 
perhaps two seconds. 

354. Since these eclipses are gradual phenomena, the determination 
of the exact moment of a satellite's disappearance or reappearance is 
very difficult, and this renders the result somewhat uncertain. Prof. E. 
C. Pickering of Cambridge has proposed to utilize photometric observa- 
tions for the purpose of making the determination more precise, and 
two series of observations of this sort and for this purpose are now 
nearly completed, one in Cambridge, and the other at Paris under 
the direction of: Cornu, who has devised a similar plan. Pickering- 
has also applied photography to the observation of these eclipses with 
encouraging success. 

355. The Distance of the Sun determined by the " Light- 
equation." — Until 1849 our only knowledge of the velocity of 
light was obtained from such observations of Jupiter's satel- 
lites. By assuming as known the earth's distance from the sun, 
the velocity of light can be obtained when we know the time 
occupied by light in coming from the sun. At present, how- 
ever, the case is reversed. We can determine the velocity of 
light by two independent experimental methods, and with a 

1 The student's attention is specially directed to the point that the ob- 
servations of the eclipses of Jupiter's satellites give directly neither the 
velocity of light nor the distance of the sun : they give only the time re- 
quired by light to make the journey from the sun. Many elementary 
text-books, especially the older ones, state the case carelessly. 



252 SATURN. [§ 355 

surprising degree of accuracy. Then, knowing this velocity 
and the " light-equation constant," we can deduce the distance 
of the sun. According to the latest determinations the veloc- 
ity of light is 186,330 miles per second. Multiplying this by 
499 we get 92,979,000 miles for the sun's distance (compare 
Art. 127). 

SATURN. 

356. This is the most remote of the planets known to the 
ancients. It appears as a star of the first magnitude (out- 
shining all of them, indeed, except Sirius), with a steady, 
yellowish light, not varying much in appearance from month 
to month, though in the course of 15 years it alternately gains 
and loses nearly 50 per cent of its brightness with the chang- 
ing phases of its rings : for it is unique among the heavenly 
bodies, a great globe attended by eight satellites and sur- 
rounded by a system of rings, which has no counterpart else- 
where in the universe so far as known. 

Its mean distance from the sun is about 9^- astronomical 
units, or 886,000000 miles ; but the distance varies nearly 
100,000000 miles on account of the considerable eccentricity 
of the orbit (0.056). Its nearest opposition approach to the 
earth is about 774,000000 miles, while at the remotest con- 
junction it is 1028,000000 miles away. The inclination of the 
orbit to the ecliptic is about 2|°. The sidereal period is about 
29^- years, the synodic period being 378 days. 

357. Dimensions, Mass, Etc. — The apparent mean diameter 
of the planet varies according to the distance from 14" to 20". 
The planet is more flattened at the poles than any other 
(nearly -j^), so that while the equatorial diameter is about 
75,000 miles, the polar is only 68,000 : the mean diameter, 

therefore, ( ""*" ), is not quite 73,000, — a little more than 
nine times the diameter of the earth. Its surface is about 84 



§357] SURFACE, ALBEDO, SPECTRUM. 258 

times that of the* earth, and its volume 770 times. Its mass is 
found (by means of its satellites) to be 95 times that of the 
earth, so that its mean density comes out only one-eighth that 
of the earth, actually less than that ofivater! It is by far the 
least dense of all the planetary family. 

Its mean superficial gravity is about 1.2 times gravity upon 
the earth, varying, however, nearly 25 per cent between the 
equator and the pole. It rotates on its axis in about 10 
hours, 14 minutes, as determined by Hall in 1876 from a 
white spot that for a few weeks appeared upon its surface. 
The observations of Stanley Williams in 1893, while generally 
confirming Hall's result, furnish evidence that spots in dif- 
ferent latitudes have slightly different periods. 

The equator of the planet is inclined about 27° to the plane 
of its orbit. 

358. Surface, Albedo, Spectrum. — The disc of the planet, 
like that of Jupiter, is shaded at the edge, and like Jupiter it 
shows a number of belts arranged parallel to the equator. The 
equatorial belt is very bright (not relatively quite so much so, 
however, as represented in Fig. 87), and is often of a delicate 
pinkish tinge. The belts in higher latitudes are comparatively 
faint and narrow, while just at the pole there is usually a cap 
of olive green. Occasionally there are slight irregularities in 
the edges of the belts. 

Zollner makes the mean albedo of the planet 0.52, about the 
same as that of Venus. 

The planet's spectrum is substantially like that of Jupiter, 
but the dark bands are rather more pronounced. These bands, 
however, do not appear in the spectrum of the ring, which 
probably has very little atmosphere. As to the physical con- 
dition and constitution of the planet, it is probably much like 
Jupiter, though it does not seem to be " boiling" quite so 
vigorously. 



254 



SATURN. 



[§358 




Fig. 87. — Saturn and his Rings. 



§ 359 ] THE RINGS. 255 

359. The Rings. — The most remarkable peculiarity of the 
planet is its ring system. The globe is surrounded by three 
thin, flat, concentric rings, like circular discs of paper pierced 
through the centre. They are generally referred to as A, B, 
and 0, A being the exterior one. 

Galileo h alf discovered them in 1610; that is, he saw with his 
little telescope two appendages on each side of the planet; but he 
could make nothing of them, and after a while he lost them. The 
problem remained unsolved for nearly 50 years, until Huyghens ex- 
plained the mystery in 1655. Twenty years later D. Cassini discovered 
that the ring is double; i.e., composed of two concentric rings, with a 
dark line of separation between them ; and in 1850 Bond of Cambridge, 
U.S., discovered a third "dusky" or "gauze" ring between the prin- 
cipal ring and the planet. (It was discovered a fortnight later, but 
independently, by Dawes in England.) 

The outer ring, A, has a diameter of about 168,000 miles, 
and a width of about 10,000. Cassini's division is about 1000 
miles wide ; the ring, B, which is much the broadest of the 
three, is about 17,000. The semi-transparent ring, C, has a 
width of about 9000 miles, leaving a clear space of from 9000 
to 10,000 miles in width between the planet's equator and its 
inner edge. Their plane coincides with that of the planet's 
equator. The thickness of the rings is extremely small, — 
probably not over 100 miles, as proved by the appearance 
presented, when once in 15 years we view them edgewise. 

360. Phases of the Rings. — The rings are inclined about 
28° to the ecliptic, and, of course, maintain their plane parallel 
to itself at all times. Twice in a revolution of the planet, 
therefore, this plane sweeps across the orbit of the earth (too 
small to be shown in the figure — Fig. 88), occupying nearly a 
year in so doing ; and whenever the plane passes between the 
earth and the sun the dark side of the ring is towards us, and 
the edge alone is visible. 



256 SATURN. 



[§360 



During the year occupied by the plane of the ring in thus sweeping 
over the orbit of the earth, the earth may cross it twice, thus giving rise 
to two periods of disappearance. When the edge is exactly towards 
us only the largest telescopes can see the ring, like a fine needle of light 
piercing the planet's ball, as in the uppermost engraving of Fig. 87. 
The last disappearance was in 1891-2 j the next will be in 1906-7. 




Fig. 88. — The Phases of Saturn's Rings. 

361. Structure of the Rings. — It is now universally ad- 
mitted that they are not continuous sheets, either solid or 
liquid, but mere swarms of separate particles, each pursuing 
its own independent orbit around the planet, though all mov- 
ing nearly in a common plane. 

The idea was first suggested by. J. Cassini in 1715, but was lost 
sight of until again suggested by Bond in connection with his dis- 
covery of the semi-transparent or dusky ring; it has finally been 
established by the researches of Peirce, Maxwell, and others, that no 
continuous sheet of solid or liquid matter could stand the strain of 
rotation, while all the conditions of the problem are met by the 
meteoric hypothesis, and in 1895, Keeler, of the Allegheny Observa- 
tory, obtained a beautiful spectroscopic confirmation of the theory by 
showing, from a photograph of the spectrum of the planet and its 
rings, that the particles at the outer edge of the ring are moving more 
slowly than those at the inner edge, the velocities being respectively 
about 10.1 and 12.4 miles a second, — as they ought to be. 



§ 361 1 SATELLITES. 257 

It is a question not yet settled whether the rings constitute 
a stable system, or are liable ultimately to be broken up. 

362. Satellites. — Saturn has eight of these attendants, the 
largest of which was discovered by Huyghens in 1655. It 
looks like a star of the ninth magnitude, and is easily seen 
with a three-inch telescope. 

Four others were discovered by D. Cassini, before 1700, — two by 
Sir William Herschel, near the end of the last century, and one, Hype- 
rion, the latest addition to the planet's family, by Bond of Cambridge, 
U.S., in September, 1848 (discovered independently by Lassell, at 
Liverpool, two days later). 

Since the order of the discovery of the satellites does not agree 
with that of the order of the distance, it has been found necessary to 
designate them by the names assigned by Sir John Herschel, as fol- 
lows, beginning with the most remote, viz. : — 

Iapetus, (Hyperion), Titan, Rhea, Dione, Tethys ; 
Enceladus, Mimas. 

It will be noticed that these names, leaving out Hyperion, which 
was not discovered when the others were assigned, form a line and a 
half of a regular Latin pentameter. 

The range of the system is enormous. Iapetus has a distance of 
2,225,000 miles, with a period of 79 days, nearly as long as that of 
Mercury. On the western side of the planet, this satellite is always 
much brighter than upon the eastern, showing that, like our own moon, 
it keeps the same face towards the planet at all times, — one-half of 
its surface having a higher reflecting power than the other. 

Titan, as its name suggests, is by far the largest. Its distance is 
about 770,000 miles, and its period a little less than 16 days. It is 
probably 3000 or 4000 miles in diameter, and, according to Stone, its 
mass is ^^o °f Saturn's. The orbit of Iapetus is inclined about 10 c 
to the plane of the rings, but all of the other satellites move exactly 
in their plane, and all the five inner ones in orbits sensibly circular. 
It is not impossible, nor even improbable, that other minute satellites 
besides Hyperion may yet be discovered in the great gap between 
Titan and Tapetus. 



258 URANUS. [§ 363 



URANUS. 

363. Uranus was the first planet ever "discovered," and the 
discovery created great excitement and brought the highest 
honors to the astronomer. It was found accidentally by the 
elder Herschel on March 13, 1781, while " sweeping" the 
heavens for interesting objects with a seven-inch reflector of 
his own construction. He recognized it at once by its disc as 
something different from a star, but supposed it to be a pecu- 
liar sort of a comet, and its planetary character was not dem- 
onstrated until nearly a year had passed. It is easily visible 
to a good eye as a star of the sixth magnitude. 

Its mean distance from the sun is about 19 times that of the 
earth, or about 1800,000000 miles, and the eccentricity of its 
orbit is about the same as that of Jupiter's, making the aphe- 
lion distance nearly 70,000000 miles greater than the distance 
at perihelion. The inclination of the orbit to the ecliptic is 
very slight — only 46'. The sidereal period is 84 years, and 
the synodic, 369^ days. 

In the telescope it shows a greenish disc about 4" in diam- 
eter, which corresponds to a real diameter of about 32,000 
miles. This makes its bulk about 66 times that of the earth. 
The planet's mass is found by its satellites to be about 14.6 
times that of the earth ; so that its density and surface gravity 
are respectively 0.22 and 0.90. The albedo of the planet, ac- 
cording to Zollner, is very high, 0.64, — even a little above 
that of Jupiter. The spectrum exhibits intense dark bands in 
the red, due to some unidentified substance in the planet's at- 
mosphere, which is probably dense. These bands explain the 
marked greenish tint of the planet's light. 

The disc is obviously oval, with an ellipticity of about A 
according to the writer's observations, which are confirmed by 
those of Schiaparelli. There are no clear markings on the 
disc, but there seem to be faint traces of something like belts, 
which, most singularly and inexplicably, seem to lie, not in the 



363 J SATELLITES. 259 

plane of the satellite orbits, but at an inclination of 20° or 
so to that plane. The observations, however, are far from sat- 
isfactory or conclusive. No spots are visible from which to 
determine the planet's diurnal rotation. 

364. Satellites. — The planet has four satellites, Ariel, 
Umbriel, Titania, and Oberon, Ariel being the nearest to the 
planet. 

The two brightest, Oberon and Titania, were discovered by Sir 
William Herschel a few years after his discovery of the planet; 
Ariel and Umbriel, by Lassell in 1851. 

They are telescopically among the smallest bodies in the 
solar system, and the most difficult to see. In real size, they 
are, of course, much larger than the satellites of Mars^ very 
likely measuring from 200 to 500 miles in diameter. 

Their orbits are sensibly circular, and all lie in one plane, 
which ought to be, and probably is, coincident with the plane 
oi the planet's equator ; but the belts raise questions. 

They are very close packed also, Oberon having a distance of only 
75,000 miles, and a period of 13 days, 11 hours, while Ariel has a 
)enod of 2 days, 12 hours, at a distance of 120,000 miles. Titania, 
he largest and brightest of them, has a distance of 280,000 miles,' 
somewhat greater than that of the moon from the earth, with a period 
)f 8 days, 17 hours. 

The most remarkable thing about this system remains to be 
uentioned. The plane of their orbits is inclined 82°.2 to the 
)lane of the ecliptic, and in that plane they revolve backwards; 
r we may say, what comes to the same thing, that their orbits 
■re inclined to the ecliptic at an angle of 97°.8, in which case 
heir revolution is considered as direct. 

NEPTUNE. 

365. Discovery. — The discovery of this planet is reckoned 
ie greatest triumph of mathematical astronomy. Uranus 



260 NEPTUNE. [§ 365 

failed to move in precisely the path computed for it, and was 
misguided by some unknown influence to an extent which 
could almost be seen with the naked eye. The difference 
between the actual and computed places in 1845 was the " in- 
tolerable quantity " of nearly two minutes of arc. 

This is a little more than half the distance between the two prin- 
cipal components of the double-double star, Epsilon Lyra?, the north- 
ern one of the two little stars which form the small equilateral triangle 
with Vega (Art. 468). A very sharp eye detects the duplicity of 
Epsilon without the aid of a telescope. 

One might think that such a minute discrepancy between 
observation and theory was hardly worth minding, and that 
to consider it " intolerable " was putting the case very strongly. 
But just these minute discrepancies supplied the data which 
were found sufficient for calculating the position of a great 
world, until then unknown, and bringing it to light. As the 
result of a most skilful and laborious investigation, Leverrier 
wrote to Galle in substance : — 

"Direct your telescope to a point on the ecliptic in the constellation of 
Aquarius, in longitude 320°, and you will find within a degree of that 
place a new planet, looking like a star of about the ninth magnitude, and 
having a perceptible disc." 

The planet w r as found at Berlin on the night of Sept. 28, 
1846, in exact accordance with this prediction, within half an 
hour after the astronomers began looking for it, and within 
52 f of the precise point that Leverrier had indicated. • 

We cannot here take the space for a historical statement, further 
than to say that the English Adams fairly divides with Leverrier the 
credit for the mathematical discovery of the planet, having solved the 
problem and deduced the planet's approximate place even earlier than 
his competitor. The planet was being searched for in England at 
the time it was found in Germany. In fact, it had already been 
observed, and the discovery would necessarily have followed in a few 
weeks, upon the reduction of the observations. 



366 J ERROR OF THE COMPUTED ORBIT. 261 

366. Error of the Computed Orbit. — Both Adams and Lever- 
rier, besides calculating the planet's position in the sky, had deduced 
elements of its orbit and a value for its mass, which turned out to be 
seriously wrong. The reason was that they assumed that the new 
planet's mean distance from the sun would follow Bode's Law, a sup- 
position perfectly warranted by all the facts then known, but which, 
nevertheless, is not even roughly true. As a consequence their com- 
puted elements were erroneous, and that to an extent which has led 
high authorities to declare that the mathematically computed planet 
was not Neptune at all, and that the discovery of Neptune itself was 
simply a " happy accident." This is not so, however. While the data 
and methods employed were not by themselves sufficient to determine 
the planet's orbit with accuracy, they were adequate to ascertain the 
planet's direction from the earth. The computers informed the ob- 
servers where to point their telescopes, and this was all that was neces- 
sary for finding the planet. In a similar case the same thing could 
be done again. 

367. The Planet and its Orbit. — The planet's mean distance 
from the sun is a little more than 2800,000000 miles (instead 
of being over 3600,000000, as it should be according to Bode's 
Law). The orbit is very nearly circular, its eccentricity being 
only 0.009. Even this, however, makes a variation of over 
50,000000 miles in the planet's distance from the sun. The 
inclination of the orbit is about If °. The period of the planet 
s about 164 years (instead of 217 as it should have been ac- 
cording to Leverrier's computed orbit), and the orbital veloc- 
ty is about 3^ miles per second. 

Neptune appears in the telescope as a small star of between 
:he eighth and ninth magnitudes, absolutely invisible to the 
laked eye, though easily seen with a good opera-glass. Like 
Uranus, it shows a greenish disc, having an apparent diameter 
)f about 2".6. The real diameter of the planet is about 35,000 
niles ; but the probable error of this must be fully 500 miles. 
Che volume is a little more than 90 times that of the earth. 

Its mass, as determined by means of its satellite, is about 
8 times that of the earth, and its density 0.20. 



262 NEPTUNE. [§ 367 

The planet's albedo, according to Zollner, is 0.46, a trifle 
less than that of Saturn and Venus. 

There are no visible markings upon its surface, and nothing 
certain is known as to its rotation. 

The spectrum of the planet appears to be like that of 
Uranus, but of course is rather faint. 

It will be noticed that Uranus and Neptune form a "pair 
of twins/' very much as the earth and Venus do, being almost 
alike in magnitude, density, and many other characteristics. 

368. Satellite. — Neptune has one satellite, discovered by 
Lassell within a month after the discovery of the planet 
itself. Its distance is about 223,000 miles, and its period 
5 d , 21 h . Its orbit is inclined to the ecliptic at an angle of 
34° 48', and it moves backward in it from east to west, like 
the satellites of Uranus. It is a very small object, not 
quite as bright as Oberon, the outer satellite of Uranus. 
From its brightness, as compared with that of Neptune itself, 
we estimate its diameter as about the same as that of our 
own moon. 

369. The Solar System as seen from Neptune. — At Nep- 
tune's distance the sun itself has an apparent diameter of only 
a little more than one minute of arc, — about the diameter of 
Venus when nearest us, and too small to be seen as a disc by 
the naked eye, if there are eyes on Neptune. Its light and 
heat are there only -gfa of what we get at the earth. Still, 
we must not imagine that the Neptunian sunlight is feeble 
as compared with starlight, or even moonlight. Even at 
the distance of Neptune the sun gives a light nearly equal 
to 700 full moons. This is about 80 times the light of a 
standard candle at one metre's distance, and is abundant for 
all visual purposes. In fact, as seen from Neptune, the sun 
would look very like a large electric arc lamp, at a distance 
of a few yards. 



§ 370] TJLTRA-NEPTUNIAN PLANETS. 263 

370. mtra-Neptunian Planets. — Perhaps the breaking down of 
Bode's Law at Neptune may be regarded as an indication that the solar 
system terminates there, and that there is no remoter planet ; but of 
course it does not make it certain. If such a planet exists, however, it 
is sure to be found sooner or later, either by means of the disturbances 
it produces in the motion of Uranus and Neptune, or else by the 
methods of the asteroid hunters, although its slow motion will render 
its discovery in that way difficult. Quite possibly its discovery may 
come within a few years as a result of the photographic star-charting 
operations now just beginning. 



Xote to Art. 350. — Mr. Douglas, assistant in the Lowell Observatory 
at Flagstaff, reports (in 1897) a series of observations upon spots on the 
surfaces of the third and fourth satellites, which give times of rotation 
agreeing with their orbital periods far within the limits of error to be ex- 
pected in such observations. This makes it practically certain that both 
these satellites behave like our moon. 



264 COMETS AND METEORS. [§371 



CHAPTER XIII. 

COMETS AND METEORS. 

THE NUMBER, DESIGNATION, AND ORBITS OF COMETS. — 

THEIR CONSTITUENT PARTS AND APPEARANCE. THEIR 

SPECTRA AND PHYSICAL CONSTITUTION. — THEIR PROB- 
ABLE ORIGIN. REMARKABLE COMETS. AEROLITES, 

THEIR FALL AND CHARACTERISTICS. — SHOOTING STARS 
AND METEORIC SHOWERS. — CONNECTION BETWEEN 
COMETS AND METEORS. 

371 . From time to time bodies very different from the stars 
and planets appear in the heavens, remain visible for some 
weeks or months, pursue a longer or shorter path, and then 
vanish in the distance. These are the "comets" (from coma, 
i.e., "hair,") so called because when one of them is bright 
enough to be seen by the naked eye, it looks like a star sur- 
rounded by a luminous fog, and usually carries with it a 
streaming tail of hazy light. The large ones are magnificent 
objects, sometimes as bright as Venus and visible by day, with 
a head as large as the moon, having a train which extends from 
the horizon to the zenith, and is really long enough to reach 
from the earth to the sun. Such comets are rare, however. 
The majority are faint wisps of light, visible only with the 
telescope. 

Fig. 89 is a representation of Donates comet of 1858, which was 
one of the finest ever seen. 

In ancient times comets were always regarded with terror, — 
as of evil omen, if not personally malignant ; and the notion 



§371] 



COMETS. 



265 




. — Naked-eye View of Donati's Comet, Oct. 4, 1858. (Bond.) 

still survives in certain quarters, although the most careful 
research goes to prove that they really do not exert upon the 
^arth the slightest perceptible influence of any kind. 



266 DESIGNATION OF COMETS. [§ 371 

Thus far, our lists contain nearly 700, about 400 of which 
were observed before the invention of the telescope, and there- 
fore must have been bright. Of those observed since then, only 
a small proportion have been conspicuous to the naked eye, — 
perhaps one in five. The total number that visit the solar 
system must be enormous, for there is seldom a time when one 
at least is not in sight ; and even with the telescope we see 
only such as come near the earth and are favorably situated 
for observation. 

372. Designation of Comets. — A remarkable comet generally 
bears the name of its discoverer, or of some one who has acquired its 
" ownership," so to speak, by some important research concerning it. 
Thus we have Halley's, Encke's, and Donates comets. The common 
herd are designated only by the year of discovery, with a letter indi- 
cating the order of discovery in that year ; or, still again, by the year, 
with a Roman numeral denoting the order of perihelion passage. Thus, 
Donates comet is "Comet 1858-VL," and also " Comet/, 1858." Comet 
b is not, however, always Comet II., for Comet c may beat it in reach- 
ing perihelion. In some cases, a comet bears a double name, as the 
Pons-B rooks Comet, which was discovered by Pons in 1812, and by 
Brooks on its recent return in 1883. 

373. Duration of Visibility and Brightness. — The comet of 
1811 was observed for 17 months, the great comet of 1861 for 
a year, and Comet 1889. 1 was followed at the Lick Observatory 
for nearly two years, — the longest period of visibility yet 
recorded. On the other hand the comet is sometimes visible 
only a week or two. The average is probably not far from 
three months. 

As to brightness, comets differ widely. About one in five 
reaches the naked-eye limit, and a very few, say four or five 
in a century, are bright enough to be seen in the daytime. 
The great comet of 1882 was the last one so observed. 

374. Their Orbits. — A large majority move in orbits that 
are sensibly parabolas. Of about 270 orbits thus far com- 
puted, more than 200 are of this kind. About 75 orbits are 



§ 374] 



THEIR ORBITS. 



267 



more or less distinctly elliptical, and about half a dozen seem 
to be hyperbolas ; but hyperbolas differing so slightly from the 
parabola that the hyperbolic character is not certain in a single 
one of the cases. Comets which have elliptical orbits of course 
return at regular intervals ; the others visit the sun only once, 
and never come back. 

As in the case of a planet, three perfect observations of a 
comet's place are sufficient to determine its entire orbit. 
Practically, however, it is not possible to observe a comet 
with anything like the accuracy of a planet, nor usually with 
sufficient precision to determine certainly from three observa- 
tions whether the orbit is or is not parabolic. 




Fig. 90. — The Close Coincidence of Different Species of Cometary Orbits within the 

Earth's Orbit. 



375. The plane of the orbit and its perihelion distance can in most 
cases be fairly settled from a few observations ; but the eccentricity, 



268 THE ELLIPTIC COMETS. [§ 375 

and the major axis (with its corresponding period), require a long 
series for their determination, and are seldom ascertained with much 
precision from observations made at a single appearance of the comet. 
In that part of the comet's path which can be observed from the earth, 
the three kinds of orbits diverge but little ; indeed, they may almost 
coincide (as shown in Fig. 90.) 

It must be understood, moreover, that orbits which are sensibly 
parabolic are seldom strictly so; indeed, the chances are infinity to 
one against an exact parabola. If a comet were moving at any 
time exactly in such an orbit, then the slightest retardation due to 
the disturbing force of any planet, would change this parabola into 
an ellipse, and the slightest acceleration would make an hyperbola of 
it. (See Art. 259.) 

376. The Elliptic Comets. — There are about a dozen of the 
elliptic orbits, to which computation assigns periods near or 
exceeding a thousand years. The real character of most of 
these orbits is still rather doubtful. About 60 comets, however, 
have orbits distinctly and certainly elliptical, and about 30 
have periods of less than a hundred years. Sixteen of these 
30 comets have been actually observed at two or more returns 
to perihelion ; as to the rest of them, some are now expected 
within a few years, and some have probably been lost to ob- 
servation, either like Biela's comet, soon to be discussed, or by 
having their orbits transformed by perturbations. 

The difficulty of determining whether a particular comet is or is 
not periodic is much increased by the fact that these bodies have not 
any characteristic " personal appearance" so to speak, by which a 
given individual can be recognized whenever seen — as Saturn could 
for instance. It is necessary to depend almost entirely upon the ele- 
ments of its orbit for the identification of a returning comet, and this 
is not always satisfactory. (See Art. 377.) 

The first comet ascertained to move in an elliptical orbit was that 
known as Halley's with a period of about 76 years, its periodicity 
having been discovered by Halley in 1681. It has since been observed 
in 1759 and 1835, and is due again about 1911. The second of the 
periodic comets (in order of discovery) is Encke's, with the shortest 
period known, only 3J years. Its periodicity was discovered in 1819. 



§376] 



COMET GROUPS. 



269 



Fig. 91 shows the orbits of a number of the short-period 
comets (it would cause confusion to insert more), and also 
that of Halley's Comet. These particular comets all (except 
Halley's) have periods ranging from 3£ to 8 years, and it will 
be noticed that they all pass very near the orbit of Jupiter. 




Fig. 91. — Orbits of Short-period Comets. 



Moreover, each comet's orbit crosses that of Jupiter near one of 
its nodes (the node is marked by a short cross line) . The fact 
is extremely significant, showing that these comets at times 
come very near to Jupiter, and it points to an almost certain 
connection between that planet and these bodies. 

377. Comet Groups. — There are several instances in which 
a number of comets, certainly distinct, chase each other along 
almost exactly the same path, at an interval, usually of a few 
months or years, though they sometimes appear simultaneously. 
The most remarkable of these "comet groups" is that composed 
of the great comets of 1668, 1843, 1880, 1882, and 1887. It is 



270 COMETS. [§377 

of course nearly certain that the comets of such a " group " 
have a common origin, perhaps from the disruption of a single 
comet by the attraction of the sun or a planet. 

378. Perihelion Distance, Etc. — The perihelion distances of 
comets differ greatly. Eight of the 270 orbits approach the sun within 
less than 6,000000 miles, and four have a perihelion distance exceed- 
ing 200,000000. A single comet, that of 1729, had a perihelion dis- 
tance of more than four astronomical units, or 375,000000 miles. It 
is one of the half dozen comets possibly hyperbolic, and must have 
been an enormous one to be visible under the circumstances. There 
may, of course, be any number of comets with still greater perihelion 
distances, because as a rule we are only able to see such as come 
reasonably near to the earth's orbit, — probably only a small percent- 
age of the total number that visit the sun. 

The inclinations of cometary orbits range all the way from zero to 
90°. As regards the direction of motion, the six hyperbolic comets and 
all the elliptical comets having periods less than 100 years move direct, 
excepting only H alley's Comet and Tempel's Comet of 1866. The 
rest show no decided preponderance either way. 

379. Comets are Visitors. — The fact that the orbits of most 
comets are sensibly parabolic and that their planes have no 
evident relation to the ecliptic, apparently indicates (though 
it does not absolutely demonstrate) that these bodies do not 
in any proper sense belong to the solar system. They are 
probably only visitors. They come to us precisely as if they 
simply dropped towards the sun from an infinite distance ; 
and they leave the system with a velocity which, if no force 
but the sun's attraction acts upon them, will carry them away 
to an infinite distance, or until they encounter the attraction 
of some other sun. Their motions are just what might be ex- 
pected of ponderable masses moving in empty space between 
the stars, under the law of gravitation. 

A slightly different view is advocated by some high authorities. 
They think that our solar system in its journey through space (Art. 



§370] PHYSICAL CONSTITUTION. 271 

430) is accompanied by distant, outlying clouds of nebulous matter, 
and that they are the source and original " home " of the comets. 
It is argued that if the comets came from interstellar space the num- 
ber of hyperbolic orbits would be much greater, because we should 
meet so many more comets than would overtake us. 

380. Acceleration of Encke's Comet. — This little comet be- 
haves in an exceptional manner. It steadily shortens its 
period of 3^ years by about 2\ hours at each revolution, hav- 
ing cut it down nearly two days since its discovery in 1819. 
This effect is probably due to some resistance l encountered by 
the comet, possibly by collision with swarms of meteors. 

PHYSICAL CONSTITUTION OF COMETS. 

381. The Constituent Parts of a Comet. — (a) The essential 
part of a comet, that which is always present and gives the 
comet its name, is the Coma, or nebulosity, a hazy cloud of 
faintly luminous transparent matter. 

(6) Next we have the Nucleus, which, however, is wanting in 
many comets, and makes its appearance only when the comet 
is near the sun. It is a bright, more or less star-like point 
near the centre of <the comet, and is usually the object "ob- 
served on" in noting a comet's place. In some cases, the 
nucleus is double or even multiple. 

(c) The Tail, or Train, is a stream of light which commonly 
accompanies a bright comet, and is sometimes present even 
with a telescopic one. As the comet approaches the sun, the 
tail follows it ; but as the comet moves away from the sun, it 
precedes. It is usually, speaking broadly, directed away from 
the sun, though its precise form and position are determined 

1 It seems at first a singular paradox that resistance should shorten a 
comet's period and make it go faster. It does so by diminishing the size 
of the orbit. Every diminution of the comet's velocity will decrease a, the 
semi-major axis of its orbit; but the time of revolution is proportional to 
a', and is hence also diminished. 



272 COMETS. [§ 381 

partly by the comet's motion. It is practically certain that 
it consists of extremely rarefied matter, which is thrown off 
by the comet and powerfully repelled by the sun. It certainly 
is not — like the smoke of a locomotive or the train of a 
meteor — matter simply left behind by the comet. 

(d) Jets and Envelopes. The head of a brilliant comet is 
often veined by short jets of light, which appear to be spurted 
out of the nucleus ; and sometimes the nucleus throws off a 
series of concentric envelopes, like hollow shells, one within 
the other. These phenomena, however, are seldom observed 
in telescopic comets. 

382. Dimensions of Comets. — The volume or bulk of a comet 
is often enormous — almost beyond conception if the tail is 
included in the estimate. The head, as a rule, is from 40,000 
to 150,000 miles in diameter : a comet less than 10,000 miles 
in diameter would stand little chance of discovery, and comets 
exceeding 150,000 are rather rare, though there are a consider- 
able number on record. 

The comet of 1811 at one time had a diameter of fully 1,200000 
miles (40 per cent larger than that of the sun). The head of the 
comet of 1680 was 600,000 miles in diameter, that of Holmes's comet 
of 1892, 700,000, and that of Donati's comet aoout 250,000. 

The diameter of the head keeps changing all the time; and 
what is singular is, that while the comet is approaching the 
sun, the head usually contracts, expanding again as it recedes. 

The diameter of Encke's Comet contracts from about 300,000 miles 
(when it is 130,000000 miles from the sun) to a diameter not ex- 
ceeding 12,000 or 14,000, when it is at perihelion, at a distance of 
33,000000, the variation in bnlk being more than 10,000 to 1. No 
entirely satisfactory explanation is known, but Sir John Herschel has 
suggested that the change is merely optical, — that near the sun a part 
of the nebulous matter is evaporated by the solar heat and so becomes 
invisible, condensing and reappearing again when the comet gets to 
cooler regions. 



382] MASS OF COMETS. 273 

The nucleus usually has a diameter ranging from 100 miles 
up to 5000 or 6000, or even more. Like the comet's head, it 
also varies greatly in diameter, even from day to day; the 
changes, however, do not seem to depend in any regular way 
upon the comet's distance from the sun, but rather upon its 
activity in throwing off jets and envelopes. 

The tail of a comet, as regards simple magnitude, is by far 
its most imposing feature. Its length is seldom less than 
5,000000 or 10,000000 miles : it frequently attains 50,000000, 
and there are several cases where it has exceeded 100,000000. 

383. Mass of Comets. — While the volume of comets is thus 
enormous, their masses are apparently insignificant, in no case 
at all comparable even with that of our little earth. The 
evidence on this point, however, is purely negative : it does 
not enable us in any case to say how great the mass really is, 
but only how great it is not] i.e., it only proves that the 
comet's mass is less than a certain very small fraction of the 
earth's mass. The evidence is derived from the fact that no 
sensible perturbations are produced in the motions of the 
planets when comets come even very near them ; and yet in 
such a case the comet itself is fairly "sent kiting," showing 
that gravitation is fully operative between the comet and 
planet. 

Lexell's Comet in 1770, and Biela's Comet on several occasions, 
came so near the earth that the length of the comet's period was 
changed by several weeks, while the year was not altered by so much 
as a single second. It would have been changed by many seconds if 
the comet's mass were as much as xmnnnr ^ na ^ °^ *he ear th. At pres- 
ent this mass ( TTn nnnr °^ the ear th's mass) is very generally assumed 
as a probable " upper limit " for even a large comet. It is about ten 
times the mass of the earth's^ atmosphere, and is about equal to the 
mass of a ball of iron 150 miles in diameter. 

384. Density of Comets. — This is, of course, extremely 
small, the. mass being so minute and the volume so great. If 



274 COMETS. [§ 384 

the head of a comet 50,000 miles in diameter has a mass 
•j-q-oVo o" that of the earth, its mean density is about q-^-q of 
that of the air at the earth's surface. As for the tail, the 
density must be almost infinitely lower yet, far below that of 
the best vacuum we can make by any means known to science : 
it is nearer to an " airy nothing " than anything else we know 
of. The extremely low density of comets is shown also by 
their transparency. Small stars can be seen through the head 
of a comet 100,000 miles in diameter, even very near its 
nucleus, and with hardly a perceptible diminution of lustre. 

385. We must bear in mind, however, that the low mean density 
of a comet does not necessarily imply that the density of its constitu- 
ent parts is small. A comet may be to a considerable extent com- 
posed of small heavy bodies, and still have a low mean density, 
provided they are widely separated. There is much reason, as we 
shall see, for supposing that such is really the case, — that the comet 
is largely composed of small meteoric stones, carrying with them a 
certain quantity of enveloping gas. 

Another point should be referred to. Students often find it hard 
to conceive how such impalpable " dust clouds " can move in orbits 
like solid masses and with such enormous velocities. They forget 
that in a vacuum a feather falls as swiftly as a stone. Inter-planetary 
space is a vacuum, far more perfect than anything we can produce by 
artificial means, and in it the lightest bodies move as freely and 
swiftly as the densest, since there is nothing to resist their motion. H 
all the earth were suddenly annihilated except a single feather, the 
feather would keep on and pursue the same orbit, with the unchanged 
speed of nearly 19 miles a second. 

386. The Light of Comets. — To some extent this may be 
mere reflected sunshine, but in the main it is light emitted by 
the comet itself, under the stimulus of solar action. 

That the light depends in some way on the sun is shown by the 
fact that its intensity follows very closely the same law as the 
brightness of a planet ; i.e., the comet's brightness is ordina- 
rily proportional to the quantity — — , in which R is the dis- 



§386] 



LIGHT OF COMETS. 



275 



tance of the comet from the sun, and r its distance from the 
earth. 

But the brightness often varies rapidly and capriciously 
without any apparent reason; and that the comet is self-lumi- 
nous when near the sun is proved by its spectrum, which is 
not that of sunlight at all, but is a spectrum of bright bands, 
three of which are usually seen and have been identified 
with the spectrum of gaseous hydrocarbons, or, possibly, acet- 
ylene. This spectrum is absolutely identical with that given 
by the blue base of a candle flame ; or, better, by a Bunsen 




Fig. 92. —Comet Spectra. 

For convenience in engraving, the dark lines of the solar spectrum in the lowest strip 
of the figure are represented as bright.) 

)urner consuming ordinary coal gas. Occasionally a fourth 
>and is seen in the violet, and when the comet approaches un- 
sually near the sun, the bright lines of sodium, magnesium, 
and probably iron) sometimes appear. There seem to be 
ases, also, in which different bands replace the ordinary 



276 



COMETS. 



[§3&i 



hydrocarbon bands, and the spectrum of Holmes's comet of 
1892 was purely continuous. Mr. Lockyer maintains that as 
a regular thing the spectrum of a comet changes with its 
changing distance from the sun, but this is doubtful. 

Fig. 02 represents the ordinary comet spectrum compared with 
the solar spectrum, and with that of a candle flame. Two anomalous 
spectra also are shown in the figure. 




Fig. 93. — Head of Donati's Comet, Oct. 5, 1858. (Bond.) 



The spectrum makes it almost certain that hydrocarbon gases are 
present in considerable quantity, and that these gases are somehow 
rendered luminous ; not probably by any general heating, for there is 
no reason to think that the general temperature of a comet is high, 
but more likely by electric discharges between the solid particles, or by 
local heatings, due perhaps, as Mr. Lockyer maintains, to collisions 
between them. We are not to suppose, however, that the hydrocar- 



386] 



PHENOMENA NEAR PERIHELION. 



277 



bon gas, because it is so conspicuous in the spectrum, necessarily con* 
stitutes most of the comet's mass : more likely it is only a very small 
percentage of the whole. 

387. Phenomena that accompany the Comet's Approach to the 
Sun. — When a comet is first discovered it is usually a mere 
round, hazy cloud of faint nebulosity, a little brighter near the 
middle. As it approaches the sun, it brightens rapidly, and 
the nucleus appears. 
Then on the sunward 
side the nucleus begins 
to emit luminous jets, or 
to throw off more or less 
symmetrical envelopes, 
which follow each other 
at intervals of some 
lours, expanding and 
growing fainter, until 
they are lost in the gen- 
eral nebulosity of the 
lead. Fig. 93 shows 
the envelopes as they 
appeared in the head of 
Donati's comet of 1858. 
At one time seven of them were visible together: very few 
comets, however, exhibit this phenomenon with such symme- 
try. More frequently the emissions from the nucleus take 
the form of mere jets and streamers, as shown in Fig. 94, 
which is a drawing of the head of Tebbutt's comet of 1881. 
This was an extremely active one, continually throwing out 
ets, breaking the nucleus into fragments, or exhibiting some 
)ther unexpected appearance. 

388. Formation of the Tail. — The tail appears to be formed 
)f material which is first projected from the nucleus of the comet 
owarcls the sun, and then afterwards repelled by the sun, as illus- 




Fig. 94. — Tebbutt's Comet, 1881. (Common.) 



278 



COMETS. 



[§388 



trated by Fig. 95. At least, this theory has the great advan- 
tage over all others which have been proposed, that it not 
only accounts for the phenomena in a general way, but admits 
of being worked out in detail and verified mathematically, by 

comparing the actual size and 
form of the comet's tail, at 
different points in the orbit, 
with that indicated by the 
theory ; and the accordance is 
generally very satisfactory. 



^ To Sun 




Fig. 95. — Formation of a Comet's Tail by 
Matter expelled from the Head. 



According to this theory, the 
tail is simply an assemblage of 
repelled particles, each moving in 
its own hyperbolic orbit around 
the sun, the separate particles hav- 
ing very little connection with or 
effect upon each other, and being 
almost entirely emancipated from 
the control of the comet's head. 
Since the force of the projection is seldom very great, all these orbits 
lie nearly in the plane of the comet's orbit, and the result is that the 
tail is usually a sort of a flat, hollow, curved, horn-shaped cone, open 
at the large end, as represented by Fig. 9G. 

389. Curvature of the Tails and 
Tails of Different Types. — The 

tail is curved, because the re- 
pelled particles after leaving the 
comet's head retain their original 
motion, so that they are arranged 
not along a straight line drawn 
from the sun to the comet, but 
on a curve convex to the direc- 
tion of the comet's motion, as 
shown in Fig. 97 : but the stronger the repulsion the less the 
curvature. 




Fig. 96. 
A Comet's Tail as a Hollow Cone. 



§ 38i) ] CURVATURE OF THE TAILS. 270 

Bredichin (of Moscow) lias found that in this respect the 
trains of comets may be classified under three different types, 
as indicated by Fig. 98. 

First, the long, straight rays: they are composed of matter upon 
which the solar repulsion is from 12 to 15 times as great as the gravi- 
tational attraction, so that the particles leave the comet with a relative 
velocity of four or five miles a second, which is afterwards continu- 
ally increased until it becomes enormous. The nearly straight rays 
shown in Fig. 89 belong to this type. For plausible reasons, con- 
nected with its low density, Bredichin considers them to be composed 
of hydrogen, possibly set free by the decomposition of hydrocarbons. 
They are rather uncommon, and in no case have been bright enough 
to allow a spectroscopic test of their nature. 




Fig. 97. — A Comet's Tail at Different Points in its Orbit near Perihelion. 

The second type is the curved plume-like train, like the principal 
ail of Donati's comet. In trains of this type, supposed to be due to 
lydrocarbon vapors, the repulsive force varies from 2.2 times the gravi- 
ational attraction for particles on the convex edge of the train, to 
lalf that amount for those on the inner edge. 

Third. A few comets show tails of still a third type, short, stubby 
>rushes, violently curved, and due to matter upon which the repulsive 
orce is feeble as compared with gravity. These are assigned to 



280 UNEXPLAINED AND ANOMALOUS PHENOMENA. [§ 389 



metallic vapors of considerable density, iron perhaps, with an admix- 
ture of sodium, etc. 

The nature of the force which repels the particles of a comet is, 

of course, only a matter of 
speculation; but there is 
at present a decided pre- 
ponderance of opinion in 
favor of the idea that it 
is electrical^ though the de- 
tailed explanation is not 
easy. 

It has also been at- 
tempted to account for the 
repulsion by the direct ac- 
tion of the waves of solar 
light and heat, and again 
by an indirect action re- 
sulting from the heating of 
the surfaces of the almost 
infinitesimal particles on 
the side next the sun. 

There is no reason to 
suppose that the matter 
driven off to form the tail 
is ever recovered by the 
comet. 

390. Unexplained and 
Anomalous Phenomena. 
— A curious phenome- 
non, not yet explained, 
is the dark stripe which, 
in a large comet nearing 
the sun, runs down the 
centre of the tail, look- 
ing very much as if it 
It is certainly not a 




Bredichin's Three Types of Cometary Tails. 

were a shadow of the comet's head, 



shadow, however, because it usually makes more or less of an 




§ 390] THE NATUKE OF COMETS. 281 

angle with the sun's direction. It is well shown in Figs. 93 
and 94. When the comet is a greater distance from the sun, 
this central stripe is usually bright, as in Fig. 99. 

Not infrequently, moreover, comets possess anomalous tails, 
— usually in addition to the normal tail, but sometimes sub- 
stituted for it, — tails directed sometimes straight towards the 
sun, and sometimes at right 
angles to that direction. Then, 
sometimes, there are luminous 
" sheaths," which seem to envelop 
the head of the comet and pro- 
ject towards the sun; or little 
clouds of cometary matter which 
leave the main comet like puffs „ . , „ 

• Bright-Centred Tail of Coggia's Comet. 

of smoke from a bursting bomb, j une , 1874. 

and travel off at an angle until 

they fade away (see Fig. 100). None of these appearances are 

contradictory to the theory above stated, although not yet 

clearly included in it. 

391. The Nature of Comets. — All things considered, the 
most probable hypothesis as to the constitution of a comet is 
that its head is a swarm of small meteoric particles, widely 
separated (say pin-heads, many feet apart), each carrying with 
it a gaseous envelope, in which light is produced either by 
electric discharges or by some action due to the rays of the 
sun. As to the size of the constituent " particles," opinions 
differ widely. Some maintain that they are large rocks : Pro- 
fessor Newton calls a comet a " gravel-bank " : others say that 
it is a mere " dust-cloud." The unquestionable and close con- 
nection between meteors and comets, which we shall soon dis- 
cuss, almost compels some " meteoric hypothesis." 

392. Origin of Periodic Comets. — It is clear, as has been 
said, that the comets which move in parabolic orbits cannot 



282 THE CAPTURE THEORY. [§ j 

have originated in the solar system, but must be visitors rather 
than citizens : as to those which move in elliptical orbits, it 
is a question whether we are to regard them as native-born or 
only as naturalized. 

It is evident that, in some way, many of them stand in pe- 
culiar relations to Jupiter and other planets (see Art. 376). 

All the short period comets, i.e., those which have periods 
ranging from three to eight years, pass very close to the orbit 
of Jupiter, and are now recognized and spoken of as Jupiter's 
" comet- family." Twenty-seven are known already, of which 
fourteen have already been observed twice or oftener. Simi- 
larly, Saturn is credited with two comets ; Uranus with three 
(one of them is Tempel's comet, which is closely connected with 
the November meteors, and is next due in 1900). Finally, 
Neptune has a family of six ; among them Halley's Comet 
and two others which have returned a second time to peri- 
helion since 1880. 

393. The Capture Theory. — The generally accepted theory 
as to the origin of these " comet families " is one first sug- 
gested by La Place, — that the comets which compose them have 
been captured by the planet to which they stand related. A 
comet entering the system and passing near a planet will be 
disturbed, and either accelerated or retarded : if it is accel- 
erated, the original parabolic orbit will be changed to an 
hyperbola, and the comet will never be seen again; but if it is 
retarded, the orbit becomes elliptical, and the comet will return 
at each revolution to the place where it was first disturbed. 
After a lapse of time the planet and the comet will come 
together a second time at or near this place. The result may 
be an acceleration which will send the comet out of the system 
again ; but it is an even chance, at least, that it may be a 
retardation, and that the orbit and period will thus be further 
diminished. And this may happen over and over again, until 



§ 393] REMARKABLE COMETS. 283 

the comet's orbit falls so far inside that of the planet that it 
suffers no further disturbance to speak of. 

Given time enough and comets enough, and the ultimate 
result would necessarily be such a comet family as really 
exists. It is not permanent, however : sooner or later, if a 
captured comet is not first disintegrated, it will almost cer- 
tainly encounter its planet under such conditions as to be 
thrown out of the system in an hyperbolic orbit. 

The late K. A. Proctor declined to accept the above theory, and 
maintained with much vigor and ability the theory that comets and 
meteor swarms have been " ejected " from the great planets by erup- 
tions of some sort. We cannot here stop to discuss the theory, but 
the objections to it are serious, and probably fatal. 

394. Remarkable Comets. — Our space does not permit us 
to give full accounts of any considerable number. We limit 
ourselves to three, which, for various reasons, are of special 
interest. 

(1) Biela's Comet is (or rather was) a small comet some 
40,000 miles in diameter, at times barely visible to the naked 
eye, and sometimes showing a short tail. It had a period of 
6.6 years, and it was the second comet of short period known, 
having been discovered by Biela, an Austrian officer, in 1826 ; 
(the periodicity of Encke's Comet had been discovered seven 
year's earlier.) Its orbit comes within a few thousand miles 
of the earth's orbit, the distance varying somewhat, of course, 
on account of perturbations ; but the approach is often so close 
that if the comet and the earth should happen to come along 
at the same time there would be a collision. 

In 1832, some one started the report that such an encounter was to 
occur, and there was in consequence, a veritable panic in southern 
France, the first of the numerous " comet-scares." On this occasion, 
the comet passed the critical point nearly a month ahead of the earth, 
and was never at a distance less than 15,000000 miles. 



284 BIELA'S COMET. [§ 395 

395. At its return in 1846 it did a very strange thing, en- 
tirely unprecedented. It split into two. When first seen, on 
Nov. 28th, it was round and single. On Dec. 19th it was dis- 
tinctly pear-shaped, and ten days later it had divided, the 
duplication being first noticed in this country (at New Haven 
and Washington) some weeks before it was observed in 
Europe. The twin comets travelled along for four months at 
an almost unchanging distance of about 165,000 miles, without 
any apparent effect upon each other's motions, but both very 
active from the physical point of view, showing remarkable 
variations of brightness, and also alternations, comet A bright- 
ening up when B was faint, and vice versa. In August, 1852, 
the twins were again observed, now at a distance of about 
1,500000 miles ; but it was impossible to tell which was 
which. Neither of them has ever been seen again, though 
they must have returned many times, if still existing as comets, 
and more than once in a favorable position. 

396. There remains, however, another remarkable chapter in 
the story of this comet, though its proper place is under the 
head of meteors. In 1872, on Nov. 27th, just as the earth was 
crossing the track of the lost comet, but some millions of 
miles behind where the comet ought to be, she encountered a 
wonderful meteoric shower. As Miss Clerke expresses it, per- 
haps a little too positively, "it became evident that Biela's 
Comet was shedding over us the pulverized products of its 
disintegration." The same thing happened again in Novem- 
ber, 1885. 

It is not certain whether the meteor swarms thus encoun- 
tered were really what was left of the comet itself, or whether 
they merely follow in its path. The comet must have been 
several millions of miles ahead of the place where these meteor 
swarms were met, unless it has been set back in its orbit since 
1852 by some unexplained and improbable perturbations. But 
if the comet still exists and occupies the place it ought to, it 



§ 396] THE GREAT COMET OF 1882. 285 

cannot be found; it must have somehow lost the power of 
shining. 

The meteors connected with this comet are known both as " Bie- 
lids " and as " Andromedes," the latter name indicating that their so 
called " radiant " is in the constellation of Andromeda. 

397. The Great Comet of 1882. — This will long be remem- 
bered, not only for its magnificent beanty, bnt for the great number 
of unusual phenomena it presented. It was first seen in the southern 
hemisphere about September 3rd, but not in the northern until the 
17th, the day on which it arrived at perihelion. On that day and the 
next, it was independently discovered within two or three degrees of 
the sun near noon, by several observers who had not before heard of 
its existence. On the 17th, at the Cape of Good Hope, the observers 
followed it right up to the edge of the sun's disc, which it " transited " 
invisibly, showing neither as a light nor as a dark spot on the solar 
surface. It was visible to the naked eye in full sunshine for nearly a 
week after perihelion. It then became a splendid object in the morning 
sky, and it continued to be observed for six months. That portion of 
the orbit visible from the earth, coincides almost exactly with the or- 
bits of four other comets, — those of 1668, 1843, 1880, and 1887, with 
which it forms a " comet group," as already mentioned (Art. 377). 

The striking peculiarity of the orbits of this " comet group " is the 
closeness of their approach to the sun, their perihelion distances all 
being less than 750,000 miles, so that they pass within 300,000 miles 
of the sun's surface ; i.e., right through the corona, and with a velocity 
exceeding 300 miles a second ; and yet this passage through the corona 
does not disturb their motion perceptibly. The orbit of the comet 
of 1882, turns out to be a very elongated ellipse, with a period of about 
800 years. The period of the comet of 1880 was computed as only 
17 years, while the orbits of the other three appear to be sensibly 
parabolic. 

398. Telescopic Features. — Early in October, the comet pre- 
sented the ordinary features. The nucleus was round, a number of 
well-marked envelopes were visible in the head, and the dark stripe 
down the centre of the tail was sharply defined. Two weeks later, 
the nucleus had been broken up and transformed into a crooked 



286 



THE COMET OF 1882. 



[§ 398 



stream, some 50,000 miles in length, of live or six bright points; the 
envelopes had vanished from the head, and the dark stripe was re- 
placed by a bright central spine. 

At the time of perihelion, the comet's spectrum was filled with 
countless bright lines. Those of sodium w T ere easily recognizable, and 
continued visible for several weeks ; the other lines disappeared much 
more quickly, and were not certainly identified, although the general 
aspect of the spectrum indicated that iron, manganese, and calcium 
were probably present. By the middle of October, it had become 
simply the normal comet spectrum, with the ordinary hydrocarbon 
bands. 




Fig. 100. — The " Sheath," and the Attendants of the Comet of 1882, 



399. The Tail. — The comet was so situated that the tail was 
directed nearly away from the earth, and so w T as not seen to good 
advantage, never having an apparent length exceeding- 85°. The 
actual length, however, at one time was more than 100,000000 miles. 



§ 399] METEORS AND SHOOTING STARS. 287 

A unique, and so far unexplained, phenomenon was a faint, straight- 
edged " sheath " of light that enveloped the portions of the comet near 
the head, and projected 3° or 4° in front of it, as shown in Fig. 100. 
Moreover, there were certain shreds of cometary matter accompanying 
the comet at a distance of 3° or 4° when first seen, but gradually re- 
ceding and growing fainter. This also was something new in comet- 
ary history, though Brooks's Comet of 1889 (next to be mentioned) 
has since then done the same thing. 

399*. Brooks's Comet 1889. V. (for a time known as the 
Lexell-Brooks Comet). Comet 1889. V was a small one dis- 
covered by Brooks in July, 1889, and was soon found to be 
moving in an elliptical orbit with a period of about 7 years. 
At the Lick Observatory it was observed to have three accom- 
panying fragments. On investigating the orbit more carefully 
with the data then available, Mr. Chandler found that in 1886 
it had passed very close to Jupiter, and that its orbit had been 
greatly changed from a much larger ellipse, with a period, ac- 
cording to his calculations, of about 27 years ; and his calcu- 
lations led him to conclude that it was very probably identical 
with the lost comet of Lexell, which was observed in 1770 
(with a period which was then computed to be about 5^- years), 
but never returned. Laplace, and later, Leverrier, showed 
that it must have passed near to Jupiter in 1779, and been 
thrown into a much larger orbit. The data, however, were 
not sufficient to decide the dimensions exactly, nor at the time 
of Mr. Chandler's computation, to make his identification cer- 
tain ; but it seemed so probable, that the comet was for some 
time called the " Lexell-Brooks." It returned late in 1896, 
and from the observations in 1889 and 1896 Dr. Poor of 
Baltimore has shown that probably Chandler's identification 
cannot be maintained. At the same time the whole history of 
the investigation forms an admirable illustration of the " cap- 
ture theory." In 1889 the comet passed certainly within 
200,000 miles of Jupiter, and perhaps even closer. The motion 
of the satellites was not in the least affected (indicating the 



288 BROOKS'S COMET. [§399* 

minuteness of its mass), but it was probably at that time that 
the comet was pulled into four pieces, as observed by Barnard. 
In 1921, if it " lives " so long, i.e., if it does not become too 
much disintegrated to be still observable as a comet, it will 
again pass near to Jupiter ; and it remains to be seen what 
will happen to it then. 

Holmes's comet of 1892-3 was in many ways remarkable. When 
first discovered it was already visible to the naked eye, and was 
apparently almost stationary, fast increasing in size as if swiftly ap- 
proaching. For a time a popular impression prevailed that it was 
Biela's lost comet, and might strike the earth, which led to some- 
thing like a " newspaper panic " in certain quarters. It was, how- 
ever, really receding, and never came nearer than 150,000000 miles. 
It was never conspicuous, and had no nucleus or notable train ; but 
its bulk was enormous : at one time its diameter exceeded 700,000 
miles. It experienced many capricious changes of apparent size and 
brightness, and its spectrum was purely continuous, — a thing unprece- 
dented in comets. It moves in an orbit like that of an asteroid, with 
its perihelion just outside the orbit of Mars, and its aphelion close to 
that of Jupiter, its period being a few days less than seven years. 

399**. Photography of Comets. — It is now possible to photo- 
graph comets, and the photographs bring out numerous pecu- 
liarities and details which are not visible to the eye even with 
telescopic aid. This is especially the case in the comet's tail. 
Fig. 100* is from Hussey's photograph of Kordame's comet of 
1893, for which we are indebted to the kindness of Professor 
Holden, director of the Lick Observatory. As the camera was 
kept pointed at the head of the comet (which was moving 
pretty rapidly) the star-images during the hour's exposure are 
drawn out into parallel streaks, the little irregularities being 
due to faults of the driving-clock and vibrations of the tele- 
scope. The knots and streamers which characterize the com- 
et's tail were none of them visible in the telescope, and differ 
from those shown upon plates taken on the days preceding and 



A V" 


* - 


J.V v 



\ v 

\\YvJS 



\ V V 



^ V 



^ 


\ 


i 


r 




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■N\. \ 

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\\ 


, 


% 


\ 


"" \ " " 

: ■ ■ - \ % 

si, \ 


y 

A 


. V , 


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s - 








A 












'* v \ 


; :-'-•« 


l 


w\ 




V 


N^ 




,. • V 
\ 


W 

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COM 


ET RORDAME, 1892. 




Photographed by 


W. 


J. Hu 


ssky, at 


the 


Lick Observatory. 



§399**] PHOTOGRAPHY OF COMETS. 289 

following. Other plates, made the same evening a few hours 
earlier and later, indicate that the knots were swiftly receding 
from the comet's head at a rate exceeding 150,000 miles an 
hour. 

In 1892 Barnard discovered a small comet by the streak it made 
upon one of his star-plates. 

METEOKS AND SHOOTING STARS. 

400. Meteorites. — Occasionally bodies fall upon the earth 
out of the sky. Until they reach the air they are usually in- 

isible, but as soon as they enter it they become conspicuous, 
and the pieces which fall are called " Meteorites," " Aerolites," 

Uranoliths," or simply " meteoric stones." 

If the fall occurs at night, a ball of fire is seen, which moves 
ritli an apparent velocity depending upon the distance of the 
neteor and the direction of its motion. The fire-ball is generally 
allowed by a luminous train, which sometimes remains visible 
or many minutes after the meteor itself has disappeared, 
he motion is usually somewhat irregular, and here and there 
long its path the meteor throws off sparks and fragments, 
nd changes its course more or less abruptly. Sometimes it 
anishes by simply fading out in the distance, sometimes by 
ursting like a rocket. If the observer is near enough, the 
ight is accompanied by a heavy, continuous roar, emphasized 
ow and then by violent detonations. The noise is frequently 
eard fifty miles away, especially the final explosion. 1 

If the fall occurs by day, the luminous appearances are 

ainly wanting, though sometimes a white cloud is seen, and 
le train may be visible. In a few cases, aerolites have fallen 
Imost silently, and without warning. 

1 The observer must not expect to hear the explosion at the moment 
hen he sees it, since sound travels only about 12 miles a minute. Usually 
e sound is some minutes on the way. 






290 AEROLITES. [§ 401 

401. The Aerolites Themselves. — The mass that falls is 
sometimes a single piece, but more usually there are many 
fragments, sometimes numbering thousands : as the old writers 
say, "It rains stones." The pieces weigh from 500 pounds to 
a few grains, the aggregate mass occasionally amounting to 
more than a ton. 

By far the greater number of aerolites are stones, but a few, 
perhaps three or four per cent of the whole number, are masses 
of nearly pure iron more or less alloyed with nickel. 

The total number of meteorites which have fallen and been gath- 
ered into our cabinets since 1800 is about 275, — 11 of which are 
iron masses. Nearly all, however, contain a large percentage of iron, 
either in the metallic form or as sulphide. Between 25 and 30 of the 
275 fell within the United States, the most remarkable being those of 
Weston, Conn., in 1807; New Concord, Ohio, 1860; Amana, Iowa, 
1875; Emmett County, Iowa, 1879 (mainly iron) ; and Johnson County, 
Ark., 1886 (iron). 

Twenty-five l of the chemical elements have been found in 
these bodies, but not one new element, though a large number 
of new minerals appear in them, and seem to be peculiar to 
and characteristic of aerolites. The most distinctive external 
feature of a meteorite is the thin, black, varnish-like crust 
that covers it. It is formed by the fusion of the surface dur- 
ing the meteor's swift flight through the air, and in some 
cases penetrates the mass in cracks and veins. The surface is 
generally somewhat uneven, having " thumb-marks " upon it, 

— hollows probably formed by the fusion of some of the 
softer minerals. 

Fig. 101 is from a photograph given in Langley's " New Astron- 
omy," where the body is designated — perhaps a little too positively 

— as "part of a comet." 

402. Path and Motion. — When a meteor has been observed 
from a number of different stations, its path can be computed. 



1 Including helium. 



§402] 



OBSERVATION OF METEORS. 



291 



It usually first appears at au altitude of between 80 and 100 
miles and disappears at an altitude of between 5 and 10 miles. 
The length, of the path may be anywhere from 50 to 500 miles. 
The velocity ranges 
from 10 to 40 miles a 
second in the earlier 
part of its course, and 
this is reduced to one 
or two miles a second 
before the meteor dis- 
appears. 

The average velocity 
with which these bodies 
enter the air seems to be 
very near the parabolic 
velocity of 26 miles a 
second, due to the sun's 
attraction at the earth's 
distance — just as should 
be the case, if, like the 
comets, they come to us 
from inter-stellar space ; 
but more recent researches 
of Professor Xewton seem 
to show such a decided 
preponderance of direct 

motions and small inclinations to the ecliptic as would rather indicate 
on the other hand, that they are of planetary instead of stellar origin — 
perhaps minute " outriders " of the asteroid group. 









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^ 




ni^tc-St 




l^llsi! 


wSBm 

1 1 




y^ :t ~\ :; jM ! H 


''**$?& 




Mj/t • . 


|w 






i^SH 






B3 'l- v ??'Hfc '*' ■■'''**& 




•£2r*~~~'- r 


L- '. *«■■,„. 







Fig. 101. 
Fragment of one of the Amana Meteoric Stones. 



403. Observation of Meteors. — The object should be to obtain 
as accurate an estimate as possible of the altitude and azimuth of the 
meteor at moments which can be identified, and also of the time occu- 
pied in traversing definite portions of the path. By night, the stars 
furnish the best reference points from which to determine its position. 
By day, one must take advantage of natural objects and buildings to 



292 THE LIGHT AND HEAT OF METEORS. [§ 403 

define the meteor's place, the observer marking the precise spot where 
he stood, when the meteor disappeared behind a chimney for instance, 
or was seen to bnrst just over a certain twig in a tree. By taking a 
proper instrument to the place afterwards, it is then easy to translate 
such data into bearings and altitude. As to the time of flight, which 
is required in order to determine the meteor's velocity, it is usual for 
the observer to begin to repeat rapidly some familiar verse of doggerel 
when the meteor is first seen, reiterating it until the meteor disap- 
pears. Then by rehearsing the same before a clock, the number of 
seconds can be pretty accurately determined. 

404. The Light and Heat of Meteors. — These are due simply 
to the destruction of the meteor's velocity by the friction and 
resistance of the air. When a body moving with a high veloc- 
ity is stopped by the resistance of the air, by far the greater 
part of its energy is transformed into heat. Sir William 
Thomson has shown that the thermal effect in the case of a 
body moving through the air with a velocity exceeding 10 
miles a second is the same as if it were immersed in a flame 
having a temperature at least as high as that of the oxy- 
hydrogen blow-pipe ; and, moreover, this temperature is inde- 
pendent of the density of the air, — depending only on the 
velocity of the meteor. Where the air is dense, the total 
quantity of heat — i.e., the number of calories developed in a 
given time — is of course greater than where the air is rarefied ; 
but the virtual temperature of the air where it rubs against the 
surface is the same in either case. During the meteor's flight its 
surface therefore is heated to lively incandescence and melted, 
and the liquefied portions are swept off by the rush of air, con- 
densing as they cool to form the train. In some cases this train 
remains visible for many minutes, — a fact not easy to explain. 
It is hardly possible that such a smoke-like cloud should remain 
luminous by retaining its heat for so long a time, and it seems 
probable therefore that the material must be phosphorescent. 

405. Origin of Meteors. — They cannot be, as some have 
maintained, the immediate products of eruption from volcanoes, 



§405] 



SHOOTING STARS. 293 



either terrestrial or lunar, since they reach our atmosphere 
with a velocity greater than 1\ miles a second, the " parabolic 
velocity " (see Art. 507*) due to the earth's attraction. This 
indicates that they come to us from the depths of space. 
There is no certain reason for assuming that they have origin- 
ated in any way different from the larger heavenly bodies : at 
the same time many of them resemble each other so closely as 
almost to compel the surmise that these at least have a com- 
mon source. 

It is not, perhaps, impossible that such may be fragments which, 
ages ago, were shot out from now extinct lunar volcanoes, with a 
velocity which made planets of them for the time being. If so, they 
have since been travelling in independent orbits, until at last they 
encounter the earth at the point where her orbit crosses theirs. Nor 
is it impossible that some of them were thrown out by terrestrial 
eruptions when the earth was young, or from the planets, or from the 
stars. 

SHOOTING STARS. 

406. Their Nature and Appearance. — These are the swiftly 
moving, evanescent, star-like points of light, which may be 
seen every few minutes on any clear, moonless night. They 
make no sound, nor (with perhaps one exception hereafter to 
be noted) has anything been known to reach the earth's sur- 
face from them, not even in the greatest " meteoric showers." 

For this reason it is probably best to retain, provisionally at least, 
the old distinction between them and the great meteors from which 
aerolites fall. It is quite possible that the distinction has no real 
ground, — that shooting stars are just like other meteors except in 
size, being so small that they are entirely consumed in the air : but 
then, on the other hand, there are some things which favor the idea 
that the two classes of bodies differ about as asteroids do from comets. 

407. Number of Shooting Stars. — Their number is enormous. 
A single observer averages from four to eight an hour ; but if 



294 SHOOTING STARS. C§ 407 

the observers are sufficiently numerous, and so organized as to 
be sure of noting all that are visible from a given station, 
about eight times as many are counted. From this it is estima- 
ted by Professor Newton that the total number which enter our 
atmosphere daily must be between 10,000000 and 20,000000, 
the average distance between them being about 200 miles. 
Besides those which are visible to the naked eye, there is a 
still larger number of meteors which are so small as to be 
observable only with the telescope. 

The average hourly number about six o'clock in the morning 
is double the hourly number in the evening ; the reason being 
that in the morning we are on the front of the earth, as re- 
gards its orbital motion, 1 while in the evening we are in the 
rear. In the evening we see only such as overtake us. In the 
morning we see all that we either meet or overtake. 

408. Elevation, Path, and Velocity. — By observations made 
at stations 30 or 40 miles apart, it is easy to determine 
these data with some accuracy. It is found that on the aver- 
age the shooting stars appear at a height of about 74 miles, 
and disappear at an elevation of about 50 miles, after travers- 
ing a course of 40 or 50 miles, with a velocity of from 10 to 30 
miles a second, — about 25 on the average. They do not be- 
gin to be visible at so great a height as the aerolitic meteors, 
and they are more quickly consumed, and therefore do not 
penetrate the atmosphere to so great a depth. 

409. Brightness, Material, Etc. — Now and then a shooting 
star rivals Jupiter or even Venus in brightness. A consider- 
able number are like first-magnitude stars, but the great ma- 
jority are faint. The bright ones generally leave trains. 

Occasionally it has been possible to get a "snap shot," so to 



1 The earth's orbital motion at any instant is (very nearly) directed 
towards that point on the ecliptic which is 90° west of the sun. 



§ 409] PROBABLE MASS. 295 

speak, at the spectrum of a meteor, and in it the bright lines 
of sodium and magnesium (probably) are fairly conspicuous 
among many others which cannot be identified by such a hasty 
glance. 

Since these bodies are consumed in the air, all we can hope 
to get of their material is their " ashes." In most places its 
collection and identification is, of course, hopeless ; but the 
Swedish naturalist, Nordenskiold, thought that it might be 
found in the polar snows. In Spitzbergen he therefore melted 
several tons of snow, and on filtering the water he actually 
detected in it a sediment containing minute globules of oxide 
and sulphide of iron. Similar globules have also been found 
in the products of deep-sea dredging. They may be meteoric, 
but what we now know of the distance to which smoke and 
fine volcanic dust is carried by the wind makes it not im- 
probable that they may be of purely terrestrial origin. 

410. Probable Mass of Shooting Stars. — We have no way 
of determining the exact mass of such a body ; but from the 
light it emits, as seen from a known distance, an estimate can 
be formed which is not likely to be widely erroneous. 

An efficient incandescent electric lamp consumes about 150 foot- 
pounds of energy per minute, for every candle power. Assuming for 
the moment, then, that the ratio of the light (or luminous energy) to 
the total energy is the same for a meteor as for the electric lamp, we 
can compute the total energy of a meteor which shines with known 
brightness for a given number of seconds ; and we can then compute 
its mass x from its known velocity. 

If a meteor converted all its energy into light, wasting none in 
invisible rays, this calculation would give the mass several times too 
great. If, on the other hand, the meteor were only feebly luminous, 
the result would be too small. 

1 If the energy is expressed in foot-pounds (pounds of force) and the 
mass is wanted in mass-pounds, the equation for the energy is 

E = = , nearly ; whence M = • 

2 n 64 V 2 



296 SHOOTING STARS. [§ 410 

It is likely on the whole that an ordinary meteor and a good 
incandescent lamp do not differ widely in their "luminous 
efficiency," and calculations on this basis indicate that the 
ordinary shooting stars weigh only a small fraction of an 
ounce, — from a grain or tivo up to 50 or 100 grains. 

411. Effects produced by Meteors and Shooting Stars. — 

We must content ourselves with merely alluding to certain effects 
which they must theoretically produce, adding that in no case have 
such effects been found sensible to observation. 

1. In the first place, meteors add continually to the earth's mass — per- 
haps as much as 40,000 tons a year. If so, it would take about 1000 
million years to accumulate a layer one inch thick on the earth's 
surface. 

2. They diminish the length of the year : (a) by acting as a resist- 
ing medium, and so really shortening the major axis of the earth's 
orbit (like the orbit of Encke's comet) ; (b) by increasing the mass of 
the earth and sun, and so increasing the attraction between them ; 
(c) by increasing the size of the earth, and thus slackening its rota- 
tion and lengthening the day. 

Calculation shows, however, that the combined effect would hardly 
amount to more than j^q of a second in a million years. 

3. Each meteor brings to the earth a certain amount of heat, devel- 
oped in the destruction of its motion. According to the best esti- 
mates, however, all the meteors that fall upon the earth in a year 
supply no more heat than the sun does in about one-tenth of a second. 

4. They must necessarily render inter-stellar space imperfectly trans- 
parent, if, as there is every reason to suppose, they pervade it through- 
out in any such numbers as in the domain of the solar system. But 
this effect is also so small as to defy calculation. 

412. Meteoric Showers. — There are occasions when these 
bodies, instead of showing themselves here and there in the 
sky at intervals of several minutes, appear in " showers " of 
thousands; and at such times they do not move at random, but 
all their paths diverge or " radiate " from a single spot in the 
sky, known as the "radiant"; i.e., their paths produced back- 
ward all pass through it, though they do not usually start 



§412] 



METEORIC SHOWERS. 



297 



there. Meteors which appear near the radiant are apparently 
stationary, or describe paths that are very short, while those 
in the more distant regions of the sky pursue long courses. 

The "radiant" keeps its place among the stars sensibly 
unchanged during the whole continuance of the shower, for 
hours or days, it may be, and the shower is named according 
to the place of the radiant. Thus, we have the "Leonids," 
or meteors whose radiant is the constellation of Leo ; the 
" Andromedes " (or Bielids) ; the "Perseids," the "Lyricls," etc. 

Fig. 102 represents the tracks of a large number of the Leonids of 
1866, showing the position of the radiant near Zeta Leonis. 




Fig. 102. —The Meteoric Radiant in Leo, Nov. 13, 1866. 



The " radiant " is explained as a mere effect of perspective. 
The meteors are all moving in lines nearly parallel when 
encountered by the earth, and the radiant is simply the per- 
spective "vanishing point*' of this system of parallels: its 



298 METEORIC SHOWERS. [§ 412 

position depends entirely upon the direction of the motion 
of the meteors relative to the earth. For various reasons, 
however, the paths of the meteors, after they enter the air, 
are not exactly parallel, and in consequence the radiant is not 
a mathematical point, but a " spot " in the sky, often covering 
an area of three or four degrees square. 

Probably the most remarkable of all the meteoric showers that 
have ever occurred was that of the Leonids on Nov. 12th, 1833. The 
number at some stations was estimated as high as 100,000 an hour, for 
five or six hours. " The sky was as full of them as it ever is of snow- 
flakes in a storm." 

413. Dates of Meteoric Showers. — Meteoric showers are 
evidently caused by the earth's encounter with a swarm of 
meteors, and since this swarm pursues a regular orbit around 
the sun, the earth can meet it only .when she is at the point 
where her orbit cuts the path of the meteors : this, of course, 
must always happen on or near the same day of the year, 
except as in the process of time the meteoric orbits shift 
their positions on account of perturbations. The Leonid 
showers^ therefore, always appear on the 13th of November, 
within a day or two ; and the Andromedes on the 27th or 28th 
of the same month. 

In some cases the meteors are distributed along their whole 
orbit, forming a sort of ring and rather widely scattered. In 
that case the shower recurs every year and may continue for 
several days, as is the case with the Perseids, or August meteors. 
On the other hand, the flock may be concentrated, and then the 
shower will occur only when the earth and the meteor-swarm 
both arrive at the orbit-crossing together. This is the case 
with both the Leonids and the Andromedes. The showers 
then occur, not every year, but only at intervals of several 
years, and always on or near the same day of the month. 
For the Leonids, the interval is about 33 years, and for the 
Bielids, usually 13. 

1 In 1892 a shower of them occurred on November 23. 



§ 413 ] THE MAZAPIL METEORITE. 299 

The meteors which belong to the same group have certain family 
resemblances. The Perseids are yellow, and move with medium 
velocity. The Leonids are very swift (we meet them), and they are 
of a bluish green tint, with vivid trains. The Bielids are sluggish 
(they overtake the earth), are reddish, being less intensely heated 
than the others, and they usually have only feeble trains. 

414. The Mazapil Meteorite. — As has been said, during these 
showers no sound is heard, no sensible heat perceived, nor do any 
masses reach the ground ; with one exception, however, that on Nov. 
27th, 1885, a piece of meteoric iron fell at Mazapil, in northern Mex- 
ico, during the shower of Andromedes which occurred that evening 
(Art. 396). Whether the coincidence is accidental or not, it is certainly 
interesting. Many high authorities speak confidently of this piece of 
iron as being a piece of Biela's comet itself ; and this brings us to one 
of the most remarkable discoveries of nineteenth century astronomy. 

415. The Connection between Comets and Meteors. — At the 

time of the great meteoric shower of 1833, Professors Olmsted 
and Twining, of New Haven, were the first to recognize the 
" radiant/' and to point out its significance as indicating the 
existence of a sivarm of meteors revolving around the sun in a 
permanent orbit. Olmsted even went so far as to call the body 
a " comet" Others soon showed that in some cases, at least, 
the meteors must be distributed in a complete ring around the 
sun, and Erman of Berlin developed a method of computing 
the meteoric orbit when its radiant is known. In 1864 Profes- 
sor Newton of New Haven showed by an examination of the 
old records that there had been a number of great meteoric 
showers in November, at intervals of 33 or 34 years, and he 
predicted confidently a repetition of the shower on November 
13th or 14th, 1866. The shower occurred as predicted, and 
was observed in Europe ; and it was followed by another in 
1867 which was visible in America, the meteoric swarm being 
extended in so long a procession as to require more than two 
years to cross the earth's orbit. The researches of Newton 
supplemented by those of Adams showed that the swarm was 
moving in a long ellipse with a 33-year period. 



300 



METEORS AND COMETS. 



[§416 



416. Identification of Meteoric and Cometary Orbits. — With- 
in a few weeks after the shower of 1866 it was shown by 
Leverrier and Oppolzer that the orbit of these meteors was 
identical with that of a faint comet known as TempePs, observed 
a year before ; and about the same time, in fact a few weeks 
earlier, Schiaparelli showed that the Perseids, or August me- 
teors, move in an orbit identical with that of the bright comet 
of 1862, known as Tattle's. 

Now a single coincidence might be accidental, but hardly 
two. Five years later came the shower of Andromedes, fol- 
lowing in the track of Biela's comet; and among the more 
than a hundred distinct meteor swarms, now recognized, Prof. 




Fig. 103. — Orbits of Meteoric Swarms. 



Alexander Herschel finds five others which are similarly re- 
lated, each to its special comet. It is no longer possible to 
doubt that there is a real and close connection between these 
comets and their attendant meteors. 

Fig. 103 represents four of these cometo-meteoric orbits. 



§417] 



NATURE OF THE CONNECTION. 



301 



417. Nature of the Connection. — This cannot be said to be 
ascertained. In the case of the Leonids and the Andromedes, 
the meteoric swarm follows the comet. But this does not seem 
to be so in the case of the Perseids, which scatter along more 
or less abundantly every year. 

The prevailing belief seems to be at present that the comet 
itself is only the thickest part of the meteoric swarm, and that 
the clouds of meteors scattered along its path are the result of 
its disintegration. 

It is easy to show that if a comet really is such a swarm, it must 
gradually break up more and more at each return to perihelion and 
disperse its constituent particles along its path, until the compact 
swarm has become a diffuse ring. The longer the comet has been 




Fig. 104. — Origin of the Leonids. 

moving around the sun, the more uniformly the particles will be 
distributed. The Perseids are supposed, therefore, to have been in 
the system for a long time, while the Leonids and Andromedes are 
believed to be comparatively newcomers. Leverrier, indeed, has gone 
so far as to indicate the year 126 a.d. as the time at which Uranus 
captured Tempel's comet, and brought it into the system (as illus- 



302 MR. lockyer's HYPOTHESIS. [§ 417 

trated by Fig. 104). But the theory that meteoric swarms are the 
product of cometary disintegration assumes the premise that comets 
enter the system as compact clouds, which, to. say the least, is not yet 
certain. 

418. Mr. Lockyer's Meteoric Hypothesis. — Within the last 
eight or ten years Mr. Lockyer has been enlarging greatly the 
astronomical importance of meteors. The probable meteoric 
constitution of the zodiacal light (Art. 343), as well as of 
Saturn's rings, and of the comets, has long been recognized y 
but he goes much farther and maintains that all the heavenly 
bodies are either meteoric swarms, more or less condensed, or 
the final products of such condensation ; and upon this hypoth- 
esis he attempts to explain the evolution of the planetary 
system, the phenomena of variable and colored stars, the 
various classes of stellar spectra, and the forms and structure 
of the nebulae, — indeed, pretty much everything in the 
heavens from the Aurora Borealis to the sun. As a " working 
hypothesis " his theory is unquestionably suggestive and has 
attracted much attention, but it does not bear criticism in all 
its details. 



§ 419] THE STARS. 303 



CHAPTER XIV. 

THE STARS. 

THEIR NATURE, NUMBER, AND DESIGNATION. — STAR- 
CATALOGUES AND CHARTS. — PROPER MOTIONS AND 
THE MOTION OT THE SUN IN SPACE. — STELLAR PAR- 
ALLAX. — STAR -MAGNITUDES. — VARIABLE STARS. 

STELLAR SPECTRA. 

419. The solar system is surrounded by an immense void, 
peopled only by meteors. If there were any body a hundredth 
part as large as the sun within a distance of a thousand astro- 
nomical units, its presence would be indicated by considerable 
perturbations of Uranus and Neptune. The nearest star, as 
far as our present knowledge goes, is one whose distance is 
more than 200,000 units, — so remote that, seen from it, the 
sun would look about like the Pole-star, and no telescope yet 
constructed would be able to show a single one of all the 
planets of the solar system. 

The spectra of the stars indicate that they are bodies like 
our sun, incandescent, shining each with its own peculiar light. 
Some are larger and hotter than the sun, others smaller and 
cooler ; some, perhaps, hardly luminous at all. They differ 
enormously among themselves, not being, as was once thought, 
as much alike as individuals of the same race, but differing as 
widely as animalcules from elephants. 

420. Number of the Stars. — Those that are visible to the 
eye. though numerous, are by no means countless. • If we take 



304 CONSTELLATIONS. [§ 420 

a limited region, as, for instance, the bowl of " The Dipper/ 1 
we shall find that the number we can see within it is not very 
large, — hardly a dozen. In the whole celestial sphere, the 
number of stars bright enough to be distinctly seen by an 
average eye is only between 6000 and 7000, — and that in a 
perfectly clear and moonless sky : a little haze or moonlight 
w T ill cut down the number full one-half. At any one time, not 
more than 2000 or 2500 are fairly visible, since near the hori- 
zon the small stars (which are vastly the most numerous) dis- 
appear. The total number which could be seen by the ancient 
astronomers well enough to be observable with their instruments 
is not quite 1100. 

With even the smallest telescope the number is enormously 
increased. A common opera-glass brings out at least 100,000, 
and with a 2^-inch telescope, Argelander made his "Durch- 
musterung" of the stars north of the equator, more than 
300,000 in number. The Lick telescope, 36 inches in diameter, 
probably reaches about 100,000000. 

421. Constellations. — The stars are grouped in so-called 
" constellations," many of which are extremely ancient, all 
those of the Zodiac and all those near the northern pole being 
of pre-historic origin. Their names are for the most part drawn 
from the Greek and Roman mythology, many of them being 
connected in some way or other with the Argonautic expedi- 
tion. In some cases the eye, with the help of a lively imagi- 
nation, can trace in the arrangement of the stars a vague 
resemblance to the object which gives name to the constella- 
tion, but generally no reason is obvious for either its name or 
its boundaries. 

Of the 67 constellations now generally recognized, 48 have 
come down from Ptolemy, the others having been formed by 
later astronomers to embrace stars not included in the old con- 
stellations, and especially to provide for the stars near the 
southern pole. Many other constellations have been proposed 
at one time or another, but since rejected as useless or imper- 



M 2 *] DESIGNATION OF THE STABS. ;J > ( ^"> 

tinent, though a few have obtained partial acceptance and at 

present find a place upon some maps. 

A thorough knowledge of these artificial star groups and of the 
names and places of the stars that compose them, is not at all essen- 
tial even to an accomplished astronomer; but it is a matter of great 
convenience to be acquainted with the principal constellations, and to 
be able to recognize at a glance the brighter stars, — 50 to 100 in 
number. This amount of knowledge is easily obtained in three or 
four evenings by studying the heavens in connection with a good 
celestial globe, or with star-maps — taking care, of course, to select the 
evenings in different seasons of the year, so that the whole sky may 
be covered. In the Uranography, which forms a supplement to this 
volume, we give a brief description of the various constellations, and 
directions for tracing them by the help of small star-maps, which are 
quite sufficient for this purpose, though not on a scale large enough 
to answer the needs of detailed study. For reference purposes 1 , the 
more elaborate atlases of Proctor, Heis, or Klein, are recommended. 

422. Designation of the Stars. — There are various ways of 
designating particular stars. 

(a) By Names. About sixty of the brighter stars have 
names of their own 

These names are partly of Latin and Greek origin (e.g., Capella, 
Sirius, Arcturus, Procvon, Regulus, etc.), and partly Arabic (e.g., 
Aldebaran, Vega, etc.). 

(b) By the Star's Place in the Constellation. This was the 
usual method employed by Ptolemy for designating stars. 

Thus, Spica is the star in the " spike of icheat " that Virgo carries ; 
Cor Leonis (the lion's heart) is a synonym for Regulus ; and Cyno- 
sure means "clog's tail "; since Ursa Minor was apparently a dog in the 
days of the early Greek astronomers, who gave that name to the star 
which is x\o\n the Pole-star. 

(c) By Constellation and Letters. In 1603, Bayer, in pub- 
lishing his star-map, adopted an excellent plan, ever since 
followed, of designating the stars in a constellation by the 

1 An excellent star-atlas by Professor Upton has lately been published 
by Ginn & Co. 



306 STAR-CATALOGUES. [§ 422 

letters of the Greek alphabet. The letters are ordinarily 
applied nearly in the order of brightness, Alpha (a) being the 
brightest star of the constellation, and Beta (/?) the next 
brightest, etc. But they are sometimes applied to the stars in 
their order of position rather than in that of brightness. 

When the stars of a constellation are so numerous as to exhaust 
the letters of the Greek alphabet, the Roman letters are next used, 
and then, if necessary, we employ the numbers which Flamsteed as- 
signed a century later. At present every naked-eye star can be re- 
ferred to and identified by its letter or number in the constellation to 
which it belongs. 

(d) By Catalogue Number. Of course the preceding meth- 
ods all fail in the case of telescopic stars. To such we refer as 
number so-and-so of some one's catalogue : thus, LI. 21,185 is 
read "Lalande, 21,185," and means the star that is so numbered 
in Lalande's catalogue. At present, somewhere from 600,000 
to 800,000 stars are contained in our catalogues, so that (except 
in the Milky Way) every star visible in a three-inch telescope 
can be found and identified in one or more of them. 

Synonyms. Of course all the bright stars which have names 
have letters also, and are sure to be found in every catalogue 
which covers their part of the heavens. A conspicuous star, 
therefore, has usually many "aliases," and sometimes great 
care is necessary to avoid mistakes on this account. 

423. Star-Catalogues. — These are lists of stars, giving their 
positions (i.e., their right ascensions and declinations, or lati- 
tudes and longitudes), and usually also indicating their so- 
called " magnitudes " or brightness. 

The first of these star-catalogues was made about 125 b.c. by Hip- 
parchus of Bithynia (the first of the world's great astronomers), 
giving the latitude and longitude of 1080 stars. This catalogue was 
republished by Ptolemy, 250 years later, the longitudes being corrected 
for precession ; and during the middle ages several others were made 
by the Arabic astronomers and those that followed them. 



§ 423 J STELLAR PHOTOGRAPHY. 307 

The modern catalogues are numerous. Some, like Argelander's 
" Durchmusterung," already referred to, give the place of a great 
number of stars rather roughly, merely as a means of ready identifica- 
tion ; others are " catalogues of precision/' like the Pulkowa and 
Greenwich catalogues, which give the places of only a few hundred 
so-called " fundamental stars," determined as accurately as possible, 
each star by itself. The immense catalogue of the German Astrono- 
mische Gesellschaft, now in process of publication, will contain accu- 
rate places of all stars above the 9th magnitude north of 15° South 
Declination. The observations, by numerous co-operating observato- 
ries, have occupied nearly 20 years, but are at last finished. 

424. Mean and Apparent Places of the Stars. — The modern 
star-catalogue contains the mean right ascension and declination of its 
stars at the beginning of some designated year ; i.e., the place the star 
would occupy if there were no equation of the equinoxes, nutation, or 
aberration. To get the actual (apparent) right ascension and decli- 
nation of a star for some given date (which is what we always want in 
practice), the catalogue place must be "reduced" to that date; that 
is, it must be corrected for precession, aberration, etc. The operation 
is, however, a very easy one with modern tables and formulae, involv- 
ing perhaps from five to ten minutes' work. ■ 

425. Star-Charts and Stellar Photography. — For some pur- 
poses, accurate st&T-charts are even more useful than cata- 
logues. The old-fashioned and laborious way of making such 
charts was by " plotting " the results of zone observations, but 
at present it is being done by means of photography, vastly 
better and more rapidly. A co-operative campaign began in 
1889, the object of which is to secure a photographic chart of 
all the stars down to the 14th magnitude. The work is now 
(1897) well advanced, more than half the necessary 23,000 
negatives having been already made. 

One of the most remarkable things about the photographic 
method is that with a good instrument there appears to be no 
limit to the faintness of the stars that can be photographed : 
by increasing the time of exposure, smaller and smaller stars 



308 



STELLAR PHOTOGRAPHY. 



[§425 




Fig. 105. — Photographic Telescope of the Paris Observatory. 



§ ±25] PROPER MOTIONS. 309 

are continually reached. With the ordinary plates and ex- 
posure-times not exceeding twenty minutes, it is now possible 
to get distinct impressions of stars that the eye cannot possi- 
bly see with the telescope employed. 

Fig. 105 represents the photographic telescope (14 inches aperture 
and 11 feet focus) of the Paris Observatory. The others engaged in 
this star-chart campaign are all of identical optical power. An inde- 
pendent campaign, under the direction of Professor Pickering, is also 
in progress with an instrument of 21 inches aperture, but of the same 
focal length. This "Bruce telescope" 1 (named after its generous 
donor, Miss Bruce of New York) has a four-lens objective, like that 
of an ordinary camera, and has a wide field of view. It is at present 
(1897) mounted at Arequipa, Pern. 

STAR MOTIONS. 

426. The stars are ordinarily called ''fixed," in distinction 
from the planets or " wanderers" because they keep their posi- 
tions and configurations sensibly unchanged w T ith respect to 
each other for long periods of time. Delicate observations, 
however, separated by sufficient intervals, have demonstrated 
that the fixity is not absolute, but that the stars are all really 
in motion ; and by the spectroscope the rate of motion towards 
or from the earth can in some cases be approximately meas- 
ured. In fact, it appears that their velocities are of the same 
order as those of the planets : they are flying through space 
incomparably more swiftly than cannon-balls, and it is only 
because of their inconceivable distance from us that they 
appear to change their places so slowly. 

427. Proper Motions. — If we compare a star's position (right 
ascension and declination), as determined to-day, with that 
observed a hundred years ago, it will always be found to have 
changed considerably. The difference is due in the main to 
precession, nutation, and aberration. Those, however, are none 
of them real motions of the stars, but are only apparent dis- 



310 PROPER MOTIONS. [§ 42 ? 

placements, and moreover are "common" ; i.e., they are shared 
alike by all the stars in the same part of the sky. But after 
allowing for all these " common " and apparent motions of a 
star, it generally appears that within a century the star has 
really changed its place more or less with reference to others 
near it, and this real shifting of place is called its "proper " 
motion, — the word " proper " being in this case the antithesis 
of "common." Of two stars side by side in the same tele- 
scopic field of view, the proper motions may be directly oppo- 
site, while, of course, the common motions will be sensibly 
the same. 

Even the largest of these proper motions is very small. 
The maximum at present known, that of the so-called " run- 
away star," 1830 Groombridge, is only 7 n a year. 1 (This star 
is not visible to the naked eye.) 

The proper motions of bright stars average higher than 
those of the smaller, as might be expected, since on the aver- 
age they are probably nearer. For the first-magnitude stars 
the average is about one quarter of a second annually, and for 
the sixth-magnitude stars — the smallest visible to the naked 
eye — it is about one twenty-fifth of a second. These motions 
are always sensibly rectilinear. 

They were first detected in 1718 by Halley, who found that since 
the time of Hipparchus the star Arctums had moved towards the 
south nearly a whole degree, and Sirius about half as much. 

428. Real Motions of the Stars. — The " proper motion " of 
a star gives us very little knowledge as to the star's real mo- 
tion in miles per second, unless we know the star's distance ; 
nor even then unless we also know its rate of motion towards 
or from us. The proper motion derived from the comparison 
of the catalogues of different dates is only the angular value 

1 About a dozen stars are known to have an annual proper motion 
exceeding 3", and about 150 exceed 1". 



To t he E arth 



§428] MOTION IN LINE OF SIGHT. 311 

of that part of the whole motion which is perpendicular to 
the line of vision. A star moving straight towards or from 
the earth has no "proper motion" at all in the technical sense; 
i.e. j no change of apparent place which can be detected by 
comparing observations of its position. 

Fig. 106 illustrates the subject. If a star really moves in a 
year from A to B, it will seem to an observer at the earth to have 
moved over the line Ab, and the proper motion (in seconds of arc) 

will be 206,265 X — . Since Ab cannot be greater than AB, 

Distance 
we can in some cases fix a minor limit to the star's velocity. We 
know, for instance, that the distance of 1830 Gr. is certainly not less 
than 2,000000 astronomical units ; and therefore, since Ab subtends 

an angle of 7" at the earth, its length must at least equal — "' — 

astronomical units, which cor- 
responds to a velocity of more 
than 200 miles a second. How 
much greater the velocity (along 
the line AB) really is, cannot & & 

be determined until we know 

. . ., , ,. . Components of a Star's Proper Motion. 

how much the star s distance 

exceeds 2,000000 units, and how rapid is the motion along Aa. 

In many cases a number of stars, in the same region of the 
sky have a motion practically identical, making it almost cer- 
tain that they are really neighbors and in some way connected, 
— probably by community of origin. In fact, it seems to be 
the rule rather than the exception, that stars which are ap- 
parently near each other are really comrades. They show, as 
Miss Clerke expresses it, a distinctly " gregarious tendency." 

429. Motion in the Line of Sight. — There is a method by 
w T hich the swift motion of a star directly towards or from us 
(now usually designated as radial motion) may be detected. 

It is not, as students sometimes think, by changes in the apparent 
size or brightness of a star. Theoretically, of course, a star which is 



312 THE SUN'S WAY. [§429 

approaching us must grow brighter ; but even the nearest star of all, 
Alpha Centauri, is so far away that if it were coining directly towards 
us at the rate of 100 miles a second, it would require more than 8000 
years to make the journey, and in 100 years its apparent brightness 
would only change about 2 per cent, — far too little to be noted by 
the eye. 

It is by means of the spectroscope. If a star is approaching 
us, the lines of its spectrum will apparently be shifted towards the 
violet, according to Doppler's principle (Arts. 200 and 500), 
and vice versa if it is receding from us. Visual observations 
of this sort, first made by Huggins in 1868, and since by others, 
have succeeded in demonstrating the reality of these motions 
in the line of sight, and in roughly measuring some of them. 
Vogel, of Potsdam, lias taken up the investigation photographi- 
cally, and has obtained results much more precise than any 
previously reached, having determined very satisfactorily the 
radial velocities of 51 of the brightest stars (see Table VI). 

Fig. 107 shows how one of the dark 

lines of hydrogen (the one known as 

II7) in the spectrum of Beta Ononis 

Spectrum of Rigel is displaced when compared with the 

Fig. 107.— Displacement of H y Line corresponding dark line in the spec- 

lu the Spectrum of Orionfs. ' trum of a « Geissler Tube " (Physics, 

}>. 557). The dark line of the stellar 
spectrum (bright In the negative) is shifted towards the red by an 

amount that indicates a rapid recession of the star. 

» 

For the most part these motions of the stars, so far as at 
present ascertained, seem to range between zero and 25 or 30 
miles a second, with still higher speeds in a few exceptional 

cases. 

430. The Sun's Way. — The proper motions of the stars are 
due partly to their own motions, but partly also to the motion 
of the sun, which, like the other stars, is travelling through 
space, taking with it the earth and the planets. Sir William 




§ ±30] PARALLAX AND DISTANCE OF STARS. ^^ 3 

Herschel was the first to investigate and determine the direc- 
tion of this motion a century ago. 

The principle involved is this : The motion of a star relative 
to the solar system is made up of its own real motion combined 
with the sun's motion reversed. On the whole, therefore, the 
stars will apparently drift bodily in a direction opposite to 
the sun's real motion. Those in that quarter of the sky to 
which we are approaching w r ill open out from each other, and 
those in the rear w r ill close up behind us. Again, from the 
radial motion of the stars (spectroscopically measured) a re- 
sult can be obtained. In the portion of the. heavens toward 
which the sun is moving, the stars will on the whole seem to 
approach, and in the opposite quarter, to recede. The indivi- 
dual motions lie in all directions ; but when we deal with them 
by the hundred the individual is lost in the general, and the 
prevailing drift appears. 

About twenty different determinations of the point in the 
sky towards which the sun's motion is directed have been thus 
far made by various astronomers. There is a reasonable ac- 
cordance of results, and they all show that the sun, with its 
attendant planets, is moving towards a point in the constella- 
tion of Hercules, having a right ascension of about 267° (17 
hours, 48 minutes), and a declination of about 31° north. 
This point is called the " Apex of the sun's way" 

As to the velocity of the sun's motion in space, the spectroscopic 
results, which on the whole are the most trustworthy, since they involve 
no assumptions as to the distance of the stars, indicate that it is about 
11 miles a second : but this cannot be taken as certainly determined. 

THE PARALLAX AND DISTANCE OF THE STARS. 

431. When we speak of the "parallax" of the sun, of the 
moon, or of a planet, we always mean the u diurnal" or "geocen- 
tric" parallax (Art. 147) ; i.e., the angular semi-diameter of the 
earth as seen from the body. In the case of a star, this kind 



314 PAKALLAX AND DISTANCE OF STARS. L§ 431 

of parallax is hopelessly insensible, never reaching 2-o~Wo °^ a 
second of arc. The expression " parallax of a star" always 
ref ers, on the contrary, to its " annual " or " heliocentric " par- 
allax ; i.e., the angular semi-diameter, not of the earth, but of 
the earth's orbit as seen from the star. In Fig. 108 the angle 
at the star is its parallax. 

Even this heliocentric parallax, in the case of all stars but 
a very few, is too minute to be fairly measured by our present 



Star 



Sun 



Fig. 108. — The Annual Parallax of a Star. 

instruments, never reaching a single second. In the case of 
Alpha Centauri, which is our nearest neighbor so far as known 
at present, the parallax is about 0".9 according to the earlier 
observers, but only 0".75 according to the latest authorities. 
Only four or five other cases are now known in which the 
parallax exceeds 0".3. 

432. In accordance with the principle of relative motion 
(Art. 287), every star really at rest must appear to move in 
the sky just as if it were travelling yearly around a little 
orbit 186,000000 miles in diameter, the precise counterpart of 
the earth's orbit, and with its plane parallel to the plane of 
the ecliptic. In this little orbit the star keeps always oppo- 
site to the earth, apparently moving in the opposite direc- 
tion. If the star is near the pole of the ecliptic, its " par- 
allactic orbit," as it is called, will be sensibly circular: if it 
is near the ecliptic, the orbit will be seen edge-wise as a straight 
line; while if a star is at an intermediate celestial latitude, the 
orbit will be an ellipse, which becomes more nearly circular as 
we approach the pole of the ecliptic. 



§432] THE LIGHT YEAR. 315 

If, now, we can measure the apparent size of this parallactic 
orbit in seconds of arc, the star's distance immediately follows. 
It equals 

p • 206265 

It X ~r — ? 

p ff 

in which R is the astronomical unit (the distance of the earth 
from the sun), and p n is the star's parallax in seconds of arc ; 
i.e., the angular semi-major axis of its parallactic orbit. 

For a discussion of methods, see Appendix, Arts. 521-523. 

433. Unit of Stellar Distance ; the Light Year. — The dis- 
tances of the stars are so enormous that even the radius of 
the earth's orbit, the " astronomical unit " hitherto employed, 
is too small for a convenient measure. It is better, and 
now usual, to take as the unit of stellar distance the so- 
called " light year"; i.e., the distance light travels in a year, 
which is about 63,000 l times the distance of the earth from 
the sun. 

A star with a parallax of one second is at a distance of 3.262 
light years ; and in general the distance in light years equals 

3.262 
p" ' 

So far as can be judged from the scanty data available, it 
appears that few if any stars are within a distance of three 
" light years " from the solar system ; that the naked-eye stars 
are probably for the most part within 200 or 300 years ; and 
that many of the remoter ones must be some thousands of 
years away. 

For the parallaxes of a number of stars, see Table V. of the Appendix. 



1 This number, 63,000, is found by dividing the number af seconds in 
a year by 499, the number of seconds that it requires light to travel from 
the sun to the earth. 



316 BRIGHTNESS AHD LIGHT OF STARS. [§ 434 



THE BRIGHTNESS AND LIGHT OF THE STARS. 

434. Star Magnitudes. — Hipparchus and Ptolemy arbitra- 
rily divided the stars into six classes, or so-called "magni- 
tudes," according to their brightness, the stars of the sixth 
magnitude being those which are barely perceptible by an or- 
dinary eye, while the first class comprised about twenty of 
the brightest. After the invention of the telescope, the same 
method was extended to the smaller stars, but without any 
settled system, so that the "magnitudes" assigned to telescopic 
stars by different observers are very discordant. 

435. Of course, the stars grouped under one magnitude are not ex- 
actly alike in brightness, but shade from brighter to fainter, so that 
precision requires the use of fractional magnitudes, and we now ordina- 
rily employ the decimal notation. Thus a star of magnitude 2.4 is a 
shade brighter than one whose magnitude is written 2.5. 

Heis enumerates the stars clearly visible to the naked eye, north 
of the 35th parallel of south declination, as follows : — 

First Magnitude, 14. Fourth Magnitude, 313. 

Second " 48. Fifth " 854. 

Third " 152. Sixth " 2010. 

Total, 3391. 

It will be noticed how rapidly the numbers increase for the smaller 
magnitudes. Nearly the same holds good also for telescopic stars, 
though below the tenth magnitude the rate of increase falls oif. 

436. Light Ratio and Absolute Scale of Star Magnitude. — 

The scale of magnitudes ought to be such that the "light 
ratio," or the number of times by ivhich the brightness of any star 
exceeds that of a star just one magnitude smaller, should be the 
same through its whole extent. This relation was roughly, but 
not accurately, observed by the older astronomers, and recently 
Professor Pickering at Cambridge, U.S., and Professor Pritch- 
ard of Oxford, England, have photometrically measured the 



§±36] SCALE OF MAGNITUDES. 317 

brightness of all the naked-eye stars visible in our latitude, 
and reclassified them according to the so-called " absolute 
scale/' which uses a uniform light ratio equal to the fifth root 
of one hundred (-^100 or 2.512). 

This is based upon an old determination of Sir John HerscheFs, who 
found that the average first-magnitude star is just about 100 times as 
bright as a star of the sixth magnitude — five magnitudes fainter. 
The use of this scale was first suggested by Pogson about 1-850. 

On this scale, Altair (Alpha Aquilse) and Aldebaran (Alpha 
Tauri) may be taken as standard first-magnitude stars, while 
the Pole-star and the two Pointers are very nearly of the 
standard second magnitude. 

437. Fractional and Negative Magnitudes, and General 

Equation. — For stars which are brighter than the standard first 
magnitude, we have to use fractional and even negative magnitudes. 
Thus, according to Pickering, the magnitude of Vega is 0.2, of Arc- 
turus 0.0, and of Sirius — 1.4, which means of course, that Arcturus is 
about 2\ tinies as bright as Altair, and Sirius 2.51 1 - 4 (about 3.63) 
times as bright as Arcturus, or about 9.12 times as bright as Altair. 

If b L is the brightness of the standard first-magnitude star (ex- 
pressed in candle power or any other convenient light unit), and b n is 
the brightness of a star of the n th magnitude, we have the equation : 

Log. b n = Log. &! — 0.4 (n — 1). 
Conversely, n = 1 + 2.5 (Log. b x — Log. & n ). 

The constant, 0.4, is one-fifth of the logarithm of 100 ; i.e., it is the 
logarithm of the "light ratio" of the absolute scale. 

438. Magnitudes and Telescopic Power. — If a good tele- 
scope just shows stars of a certain magnitude, then, since the 
light-gathering power of a telescope depends on the area of # 
its object-glass (which varies as the square of its diameter), 
we must have a telescope with its aperture larger in the ratio 
of V2.512 : 1, in order to show stars one magnitude smaller ; 
i.e., the aperture must be increased in the ratio of 1.59 to 1. 



318 STELLAR PHOTOMETRY. [§ 438 

A ten-fold increase in the diameter of an object-glass theoret- 
ically carries the power of vision just five magnitudes lower. 

It is usually estimated that the 12th magnitude is the limit of 
vision for a 4-inch glass. It would require, therefore, a 40-inch glass 
to reach the 17th magnitude of the absolute scale ; but on account of 
loss of light from the increased thickness of the lenses and for other 
reasons, the powers of large glasses never quite reach the theoretical 
limit. 

439. Measurement of the Brightness of Stars : Stellar Photom- 
etry. — Our space does not permit any extended discussion of this 
subject, which has of late attracted much attention. When a system 
of a few standard stars has been determined, it is possible by their 
help to arrange the other stars in a consecutive series without instru- 
ments at all, using Herschel's method of so-called " sequences" which 
consists merely in making lists of stars, 25 or 30 at a time, arranged 
in the order of brightness, taking care that some of the stars of each 
list are included in other lists. Afterwards by comparing the lists we 
can make the necessary arrangement. But to get the relative bright- 
ness of the standard stars, we must measure their brightness with instru- 
ments known as " photometers," mere estimates not being sufficient. 

440. Starlight compared with Sunlight. — Zollner and others 
have endeavored to determine the amount of light received by 
us from certain stars, as compared with the light of the sun. 
According to Zollner, Sirius gives us about t^- -- 1 o""owo* as 
much light as the sun does, and Capella and Vega about 
■5""oo"o"o~Vo"oo""o"o- According to this, a standard first-magnitude 
star, like Altair, should give us about -g- 0000 oq oooo ? an( ^ ^ 
would take, therefore, about nine billions (English) — i.e., 
about nine million million — stars of the sixth magnitude to 
do the same. These numbers, however, are very uncertain. 
The various determinations for Vega range all the way from 

600 000000 tu 40 00 0"0~0 0"0~* 

441. Assuming what is roughly, but by no means strictly, true, 
that Argelander's magnitudes agree with the absolute scale, it appears 



§441] HEAT FROM THE STARS. 319 

that the 324,000 stars of his Durchmusterung, all of them north of 
the celestial equator, give a light about equivalent to 240 or 250 first- 
magnitude stars. How much light is given by stars smaller than the 
9 \ magnitude (which was his limit) is not certain. It must vastly 
exceed that given by the larger stars. As a rough guess, we may, 
perhaps, estimate that the total starlight of both the northern and 
southern hemispheres is equivalent to about 3000 stars like Vega, or 
1500 at any one time. According to this, the starlight on a clear 
night is about fa of the light of the full moon, or about 3 3-^00 00 °f 
sunlight. More than 95 per cent of it comes from stars which are 
entirely invisible to the naked eye. 

442. Heat from the Stars. — No doubt the stars send us heat, 
and attempts have been made to measure it. Certain results that 
were supposed to have been obtained some 30 years ago have, how- 
ever, received no confirmation since, and seem improbable. They 
would make the proportion of stellar heat to solar very much greater 
than that of starlight to sunlight, and there is no reason for supposing 
that this is the case ; unless it is, the stellar heat must be far below 
the possibility of measurement by any apparatus now at our command. 

443. Amount of Light emitted by Certain Stars. — When we 

know the parallax of a star (and therefore its distance in astro- 
nomical units) it is easy to compute its real light emission as 
compared with that of the sun. It is only necessary to mul- 
tiply the light we now get from it (expressed as a fraction of 
sunlight) by the square of the star's distance. Thus, accord- 
ing to Gill, the distance of Sirius is about 550,000 units ; 
and the light we receive from it is 7000 qooooo °^ sunlight. 
Applying the principle above stated, we find that Sirius is 
really emitting more than 40 times as much light as the sun. 
As for other stars whose distance and light have been meas- 
ured, some turn out brighter and some darker than the sun ; 
the range of variation is very wide, and the sun holds appar- 
ently a medium rank in brilliance among its kindred. 

444. Why the Stars differ in Brightness. — The apparent 
brightness of a star, as seen from the earth, depends both on 



320 s VARIABLE STARS. [§ 444 

its distance and on the quantity of light it emits, and the latter 
depends on the extent of its luminous surface and upon the 
brightness of that surface ; as Bessel long ago suggested, " there 
may be as many dark stars as bright ones." Taken as a class, 
the bright stars undoubtedly average nearer to us than the 
fainter ones, and just as certainly they average larger in diam- 
eter, and also more intensely luminous. But when we compare 
a single bright star with a fainter one, we can seldom say to 
which of the three different causes it owes its superiority. 
We cannot assert that a particular faint star is smaller or 
darker or more distant than a particular bright star, unless we 
know something more than the simple fact that it is fainter. 

445. Dimensions of the Stars. — We have very little absolute 
knowledge on this subject : in a single instance, that of Algol (see 
Art. 454*), it has been possible to obtain an indirect measure, show- 
ing that that star is probably a little more than a million miles in 
diameter : considerably bulkier than the sun. The apparent, angular 
diameter of a star is probably in no case large enough to be directly 
measured by any of our present instruments. At the distance of 
Alpha Centauri the sun would have an angular diameter less than 
0."01. We shall find that in the case of binary stars of which we 
happen to know the parallax, we can determine their masses : but 
diameters, volumes, and densities are at present quite beyond our reach 
except in the single instance of Algol. 

VARIABLE STARS. 

446. Classes of Variables. — Many stars are found to change 
their brightness more or less, and are known as variable. 
They may be classified as follows : — 

I. Stars that change their brightness slowly and continu- 
ously. 
II. Those that fluctuate irregularly. 
III. Temporary stars which blaze out suddenly and then 
disappear. 



§ 446] CLASSIFICATION. 321 

IV. Periodic stars of the type of" Omicron Ceti" usually with 
a period of several months. 
V. Periodic stars of the type of " Beta Lyrce" usually having 
short periods. 

VI. Periodic stars of the "Algol type" in which the variation 
is like what might be produced if the star were peri- 
odically eclipsed by some intervening object. 

447. I. Gradual Changes. — The number of stars which are 
certainly known to be changing gradually in brightness is sur- 
prisingly small, considering that they are growing older all the 
time. On the whole, the stars present, not only in position, 
but in brightness also, sensibly the same relations as in the 
catalogues of Hipparchus and Ptolemy. 

There are, however, instances in which it can hardly be doubted 
that considerable change has occurred even within the last two or 
three centuries. Thus Bayer in 1610 lettered Castor as Alpha Gemi- 
norum, while Pollux, which he called Beta Geminorum, is now con- 
siderably the brighter : there are about a dozen other similar cases 
known, and a much larger number suspected. 

448. Missing and New Stars. — It is commonly believed that a 
considerable number of stars have disappeared since the first cata- 
logues were made, and that some new ones have come into existence. 
While it is unsafe to deny absolutely that such things may have hap- 
pened, we can say, on the other hand, that not a single case of the 
kind is certainly known. In numerous instances, stars recorded in 
the catalogues are now missing; but in nearly every case we can 
account for the fact either by a demonstrated error of observation or 
printing, or by the fact that the missing stars were planets. There is 
no case of a new star appearing and remaining permanently visible. 

449. II. Irregular Fluctuations. — The most conspicuous vari- 
able star of the second class is Eta Argus (not visible in the United 
States). It varies all the way from zero magnitude (in 1843 it stood 
next to Sirius in brightness) down to the seventh, w T hich has been 
its status ever since 1865, although in 1888 it was reported as slightly 



322 TEMPCXRAKY STARS. [§ 449 

brightening up again. Alpha Ononis and Alpha Cassiopeiae behave 
in a similar way, except that their range of brightness is small, not 
much exceeding half a magnitude. 

450. III. Temporary Stars. — There are eleven well au- 
thenticated instances of stars which have blazed up suddenly, 
and then gradually faded away. The most remarkable of 
these was that known as Tycho's Star,- which appeared in the 
constellation -of Cassiopeia in November, 1572, was for some 
days as bright as Venus at her best, and then gradually faded 
away, until at the end of 16 months it became invisible ; (there 
were no telescopes then.) It is not certain whether it still 
exists as a telescopic star : so far as we can judge, it may be 
either of half a dozen which are near the place determined by 
Tycho. There has been a curious and utterly unfounded 
notion that this star was the " Star of Bethlehem" and would 
reappear to herald the second advent of the Lord. 

A temporary star, which appeared in the constellation of 
Corona Borealis in May, 1866, is interesting as having been 
spectroscopically examined by Huggins when near its bright- 
est (second magnitude). It then showed the same bright lines 
of hydrogen which are conspicuous in the solar prominences. 
Before its outburst, it was an eighth-magnitude star of Arge- 
lander's catalogue, and within a few months it returned to its 
former low estate, which it still retains. 

In August, 1885, a sixth-magnitude star suddenly appeared 
in the great nebula of Andromeda, very near the nucleus. It 
began to fade almost immediately, and in a few months en- 
tirely disappeared. Its spectrum was sensibly continuous. 

In December 1891 a "Nova" appeared in the foot of Au- 
riga. In February it was nearly of the 4th magnitude, and 
remained visible to the naked eye for about a month. Its 
spectrum was very interesting. The bright lines were numer- 
ous, those of hydrogen and helium with the H and K of cal- 
cium, being specially conspicuous ; and each of them was 
accompanied by a dark line on the more refrangible side, as 



§ 450] TEMPOKARY STARS. 323 

if two bodies were concerned : one of them giving bright lines 
in its .spectrum and receding from us, the other, with corre- 
sponding dark lines in its spectrum, but approaching. Accord- 
ing to Vogel the relative velocity of the two masses must, if 
this is the true explanation, have exceeded 550 miles a second. 

In April the star became invisible, but brightened up again 
in the autumn, and then showed an entirely different spectrum, 
closely resembling that of a nebula. The phenomena of this 
star have led to a great deal of discussion, and cannot be said 
to have reached as yet a wholly satisfactory explanation. 

The still more recent « Novae " of 1893 and 1895 (Nova 
Carinse and Nova Normae) are peculiar in that they were de- 
tected by photography, having been recognized by Mrs. Fleming 
of the Harvard College Observatory both upon the chart-plates 
and spectrum-photographs taken at the Harvard Station in 
South America. The stars were not large enough to be seen 
by the naked eye, but their spectra appeared to be identical 
with that of Nova Aurigse, showing the same combination of 
bright lines with dark. It now seems rather probable that 
"new stars" are not really extremely rare, and it is clear that 
there are important physical resemblances between them. 

451. IV. Variables of the "Omicron Ceti" Type. — These 
objects behave almost exactly like the temporary stars, in re- 
maining most of the time faint, rapidly brightening, and then 
gradually fading away, — but they do it periodically. Omicron 
Ceti, or Mira (i.e., "the wonderful") is the type. It was dis- 
covered by Fabricius in 1596, and was the first variable known. 
During most of the time it is invisible to the naked eye, of 
about the 9th magnitude at the minimum, but at intervals of 
about 11 months it runs up to the fourth or third, or even 
second, magnitude, and then back again; .the rise is much 
more rapid than the fall. It remains at its maximum about a 
week or ten days. The maximum brightness varies very con- 
siderably, and its period, while always about 11 months, also 
varies to the extent of two or three weeks, and during the last 



324 



VABIABLE STABS. 



[§451 



few years seems to have Shortened materially. The spectrum 
of the star at its maximum is very beautiful, showing a large 
number of intensely bright lines, some of which are certainly 
due to hydrogen. 

Us "light curve" is A in Fig, 100. 




Fie, 109. — Light Curves of Variable Stars. 

A large proportion of the known variables belong to this 
class (nearly half of the whole), and a large proportion of 
them have periods which do not differ very widely from one 
year. None so far discovered exceed two years, and none are 
less than two months. Most of the periods, however, are more 
or less irregular. Some writers include the temporary stars 
in this class, maintaining that the only difference is in the 
length of period. 



J452] EXPLANATIONS OF VARIABILITY. 325 

452. Class V. Short-Period Variables. — In these the periods 
range from about o! hours (that of D Pegasi, the shortest 
known at present) to three or four weeks, and the light of the 
star fluctuates continually. Jn many eases there are two or 
more maxima in a complete period, accompanied by compli- 
cated spectroscopic phenomena much like those observed in 
Nova Aurigae. The light curves of Beta Lyrae and Eta Aquilae, 
which are typical of this class, are given at B, Fig. 109. 

453. Class VI. The Algol Type. — In this class the star re- 
mains bright for most of the time, but apparently suffers a 
periodical eclipse. The periods are mostly very short, ranging 
from ten hours to about five days. 

Algol, or Beta Per.sei. is the type star. During most of the 
time it is of the second magnitude, and it loses about five- 
sixths of its light at the time of obscuration. The fall of 
brightness occupies about 4£ hours ; the minimum lasts about 
20 minutes, and the recovery of light takes about 3£ hours. 
The period, a little less than three days, is known with great 
precision, — to a single second indeed, — and is given in con- 
nection with the light curve of the star in Fig. 109. Only 
fourteen stars of this class are known at present (1807;. 

454. Explanation of Variable Stars. — No single explanation 
will cover the whole ground. As to progressive changes, none 
need be looked for. The wonder rather is that as the stars 
grow old, such changes are not more notable. As for irregular 
changes, no sure account can yet be given. Where the range 
of variation is small fas it is in most cases; one thinks of spots 
on the surface of the star, more or less like sun spots : and if 
we suppose these spots to be much more extensive and numer- 
ous than are sun spots, and also like them to have a regular 
period of frequency, and also that the star revolves upon its 
axis, we find in the combination a possible explanation of a 
large proportion of all the variable stars. For the temporary 
stars, we may imagine either great eruptions of glowing mat- 



326 EXPLANATION OF VARIABLE STARS. [§ 454 

ter, like solar prominences on an enormous scale ; or, with 
Mr. Lockyer, we may imagine that most of the variable stars 
are only swarms of meteors, rather compact, but not yet hav- 
ing obtained the condensed condition of our sun. Stars of the 
Mira type, according to this view, owe their regular outbursts 
of brightness to the collisions due to the passage of a smaller 
swarm through the outer portions of a larger one, around 
which the smaller revolves in a long ellipse. But the great 
irregularity in the periods of variables belonging to this class 
is hard to reconcile with a true orbital revolution, which is 
usually an accurate time-keeper. Many of the spectroscopic 
phenomena of the temporary stars and of the periodic stars 
of Class IV resemble pretty closely those that appear in the 
solar chromosphere and prominences ; • suggesting in such 
cases a theory of explosion or eruption. 

In the case of the short-period variables of Class V, the 
spectroscopic phenomena in some instances rather seem to in- 
dicate the mutual interaction of two or more bodies revolving 
close together around a common centre of gravity : this is the 
case with Beta Lyrae. Others admit of simpler explanation, 
as due merely to the axial rotation of a body with large spots 
upon its surface. 

454*. Stellar Eclipses. — As to stars of the Algol type the 
most natural explanation, suggested by Goodricke more than 
a century ago, is that the obscuration is an eclipse produced 
by the periodical interposition of some opaque body between 
us and the star. 

The truth of this theory was substantially demonstrated in 1889 
by Vogel, who found by his spectroscopic observations (see Art. 429) 
that 17 hours before the minimum Algol is receding from us at the 
rate of nearly 27 miles a second, while 17 hours after the minimum 
it is coming toward us at practically the same rate. This is just what 
ought to happen if Algol had a large dark companion and the two 
were revolving around their common centre of gravity, in an almost 



§ 454*] STELLAR ECLIPSES. 327 

circular orbit, nearly edgewise towards the earth. Vogel's conclusions 
are that the distance of the dark star from Algol is about 3,250000 
miles, that their diameters are about 840000 and 1,060000 miles re- 
spectively. Furthermore, their period being 2 d 20 h 48. 9 m , it follows 
(see Art. 466) that their united mass is about two-thirds that of the 
sun, and their mean density only about one-fifth as great as his : less 
even than that of Saturn, and not much above the density of cork. 

In the case of Y Cygni, both components are about equally bright, 
so that two minima occur at each revolution, but not at equal inter- 
vals. Duner has shown that this is to be explained by the elliptical 
form of the two orbits around the common centre. 

455. Number and Designation of Variables, and their Range 
of Variation. — Mr. Chandler's catalogue of known variables 
(published in 1896) includes 393 objects, and there are also a 
considerable number of suspected variables. About 300 of 
them are clearly periodic in their variation. The rest of them 
are, some irregular, some temporary, and in respect to many 
we have not yet certain knowledge whether the variation is 
or is not periodic. 

Such variable stars as had not familiar names of their own 
before the discovery of their variability, are generally indi- 
cated by the letters E, S, T, etc.; i.e., E. Sagittarii is the 
first discovered variable in the constellation of Sagittarius; 
S. Sagittarii is the second, and so on. 

In a considerable number of the earlier discovered variables, 
the range of brightness is from two to eight magnitudes ; i.e., 
the maximum brightness exceeds the minimum from six to a 
thousand times. In the majority, however, the range is much 
less, often only a fraction of a magnitude. 

It is worth noting that a large proportion of the variables, 
especially of Classes IV. and V., are reddish in their color. 
This is not true of the Algol type. 

455*. Photography has lately come to the front as a most effective 
method of detecting variables. A very large proportion of all those 
discovered within the last eight years have been found by the com- 



328 NUMBER AND DESIGNATION OF VARIABLES. [§455* 

parison of the photographic star charts made at Cambridge and at 
their South American subsidiary stations. In many cases the photo- 
graphed spectrum of a star has attracted attention by its bright lines 
and a peculiar " colonnaded " structure marking it as "suspicious" : 
and the suspicion is usually soon justified. 

One of the most interesting and even startling results of stellar 
photography is the discovery of variable star-clusters, announced by 
Pickering, in 1895, from the study of photographs made by S. I. Bailey 
at Arequipa. A large number of negatives of several different clus- 
ters were made, and it soon appeared that while in some no changes 
were apparent, in others variable stars abound. In the cluster known 
as Messier 3 (Uranog., Art. 41) no less than 87 variables were found 
and verified. In the cluster Messier 5 (Uranog., Art. 44) nearly 50 
have been detected. The periods have not yet been accurately worked 
out, but are very short for the most part ; so that photographs taken 
only two hours apart show numerous cases where the change of 
brightness amounts to a full magnitude or more. The stars are 
mostly very small, generally below the 11th magnitude. 

In Table IV. of the Appendix, we give from Chandler's catalogue 
a list of the principal naked-eye variables which can be seen in the 
United States. The observation of variable stars is especially com- 
mended to the attention of amateurs, because with a very scanty in- 
strumental equipment, work of scientific value can be done in this 
line. The observer should put himself in communication with the 
director of some active observatory, in order to secure the proper 
discussion and publication of his results. 

STAR SPECTRA. 

456. As early as 1824, Fraunhofer observed the spectra of a 
number of bright stars, by looking at them through a small 
telescope with a prism in front of the object-glass. In 1864, 
as soon as the spectroscope had taken its place as a recognized 
instrument of research, it was applied to the stars by Huggins 
and Secchi. The former studied comparatively few spectra, 
but very thoroughly, with reference to the identification of the 
chemical constituents of certain stars. He found with cer- 
tainty in their spectra the lines of sodium, magnesium, calcium, 
iron, and hydrogen, and more or less doubtfully a number of 



§45(3] 



STAR SPECTRA. 



329 



other metals. Secchi, on the other hand, examined great num- 
bers of spectra, less in detail, but with reference to a classifi- 
cation of the stars from the spectroscopic point of view. 

457. Secchi's Classes of Spectra. — He made four classes, as 
follows : — 

I. Those which have a spectrum characterized by great in- 
tensity of the dark hydrogen lines, all other lines being compar- 
atively feeble or absent. This class comprises more than half 
of all the stars examined, — nearly all the white or bluish stars. 
Sirius and Vega are its types. 




Fig. 110. — Secchi's Types of Stellar Spectra. 

II. Those which show a spectrum resembling that of the sun ; 
i.e., with numerous fine dark lines in it. Capella (Alpha 
Aurigae) and Pollux (Beta Geminorum) are conspicuous exam- 
ples. The stars of this class are also numerous, the first and 
second classes together comprising fully seven-eighths of all 
the stars observed. 

Certain stars like Procyou and Alt air seem to be intermediate be- 
tween the first and second classes. 



330 



CLASSES OF SPECTRA. 



[§457 



III. Stars which show spectra characterized by dark bands, 
sharply defined at the upper or more refrangible edge, and 
shading out towards the red. Most of the red stars, and a 
large number of the variable stars, belong to this class. Some 
of them show also bright lines in their spectra. 

IV. This class comprises only a few small stars, which 
show, like the preceding, dark bands, but shading in the opposite 
direction; usually also they show a few bright lines. 

Fig. 110 represents the typical light curves of the four classes of 
spectra, the dark lines of the spectrum being indicated by the lines 
running downward from the contour of the curve, and the bright lines 
l»y the lines projecting upward. Yogel has modified Secchi's classifi- 
cation, and very recently Lockyer has proposed an entirely new one, 
based on his meteoric hypothesis. We give Secchi's, however, as on 
the whole the one best known and most used. 

458. Photography of Stellar Spectra. — The observation of 
these spectra by the eye is very tedious and difficult, and 
photography has of late been brought in most effectively. 
Huggins in England, and Henry Draper in this country, were 
the pioneers ; but incomparably the finest results in this line 
are those that have lately been obtained by Pickering of Cam- 
bridge, U.S., in connection with the Draper Memorial Fund. 

Pickering uses an 11- 
inch telescope, formerly 
belonging to Draper, 
with a battery of four 
enormous prisms placed 
in front of the object- 
glass, as shown in Fig. 
Ill, forming thus a 
" slitless spectroscope." 
The edges of the prisms 
are placed east and west, 
and the clock-work on 
the telescope is made to 

Fig. 111. — Arrangement of the Prisms in the Slitless t r 

run a trifle too fast or 

too slow, in order to give 




-Arrangement of the Prisms in the Slitless 
Spectroscope. 



§ 458] 



PHOTOGRAPHY OF STELLAR SPECTRA. 



331 



width to the spectrum formed upon the sensitive plate, which is 
placed at the focus of the object-glass : if the clock-work followed 
the star exactly, the spectrum would be a mere narrow streak. With 
this apparatus and an exposure of 30 minutes, spectra are obtained 
which, before enlargement, are fully three inches long from the F 
line to the ultra-violet extremity. They easily bear tenfold enlarge- 
ment, and show^ hundreds of lines in the spectra of the stars belong- 
ing to Secchi's second class. Fig. 112 is from one of these photographs 
of the spectrum of Vega. 

The great Bruce telescope (Art. 425) has also been provided with 
an object-glass prism, and with that instrument the spectra of very 
faint stars can now be reached. 



c 



KH 



h 



Hy 



1 

F 



Fig. 112. — Photographic Spectrum of Vega. 

459. The slitless spectroscope has three great advantages, — first, 
that it utilizes all the light which comes from the star to the object- 
glass, much of which, in the usual form of instrument, is lost in the jaws 
of the slit ; second, by taking advantage of the length of a large tele- 
scope, it produces a very high dispersion with even a single prism ; 
third, and most important of all, it gives on the same plate and with a 
single exposure the spectra of all the many stars whose images fall 
upon the plate. Per contra, the giving up of the slit precludes all the 
usual methods of identifying the lines of the spectrum by actually 
confronting them with comparison spectra. This makes it very dim- 
cult to utilize the photographs for some purposes of scientific w T ork. 
For instance, it has not yet been found possible to use the slitless 
spectroscope for determining the absolute motions of the stars in the 
line of sight, though Professor Pickering in 1896 devised an exceed- 
ingly ingenious method of using it to measure the relative motion of 
different stars photographed on the same plates, in such a way that 
any rapid motion of circulation among the stars of a single group 
(the Pleiades, for instance) might be detected. In the case of the 
Pleiades, however, the result was simply negative : no such relative 
motion was found. Vogel's apparatus, for this purpose (Art. 459), 
is of the ordinary form, with a slit upon which the image of the star 
is thrown. 



332 TWINKLING OF THE STARS. [§ 4<!0 

460. Twinkling or Scintillation of the Stars. — Before closing 

the discussion of starlight, a word should be added upon this subject, 
though the phenomenon is purely physical and not in the least 
astronomical. It depends both upon the irregularities of refractive 
power in the air traversed by the light on its way to the eye, and 
also on the fact that the star is optically a luminous point without 
apparent size, a fact which gives rise to " interference " phenomena. 
Planets, which have discs measurable with a micrometer, do not sensi- 
bly twinkle. The scintillation is, of course, greatest near the horizon, 
and on a good night it practically disappears at the zenith. When 
the image of a scintillating star is examined with a spectroscope, dark 
interference bands are seen moving back and forth in the spectrum. 



§ 461] DOUBLE STARS. 333 



CHAPTER XV. 

DOUBLE AND MULTIPLE STARS ; CLUSTERS AND NEBULAE. 
— THE MILKY AY AY AND THE DISTRIBUTION OF THE 
STARS IN SPACE. — THE STELLAR UNIVERSE. — COSMOG- 
ONY AND THE NEBULAR HYPOTHESIS. 

461. Double Stars. — The telescope shows numerous cases 
in which two stars lie so near each other that they can be sep- 
arated only by a high magnifying power. These are double 
stars, and at present more than 10,000 such couples are known. 
There is also a considerable number of triple stars, and a few 
which are quadruple. Fig. 113 represents some of the best- 
known objects of each class. 

The apparent distances generally range from 30" downwards, 
very few telescopes being able to separate stars closer than one- 
fourth of a second. In a large proportion of cases, perhaps one- 
third of all, the two components are very nearly equal ; but in 
many they are very unequal ; in that case (never when they 
are equal) they often present a contrast of color, and when 
they do, the smaller star, for some reason not yet known, 
always has a tint higher in the spectrum than that of the 
larger : if the larger is reddish or yellow, the small star will 
be green, blue, or purple. Gamma Andromedae and Beta 
Cygni are fine examples for a small telescope. 

The "distance" and "position angle" of a double star are 
usually measured with the filar micrometer (Appendix, Art. 
542), the position angle being the angle made at the larger 
star between the hour-circle and the line which joins the stars. 
This angle is always reckoned from the north through the 
east, completely around the circle ; i.e., if the smaller star were 
northwest of the larger one, its position angle would be 315°. 



834 STARS OPTICALLY AND PHYSICALLY DOUBLE. [§ 462 

462. Stars Optically and Physically Double. — Stars may be 
double in two ways, optically and physically. In the first 

case- they arc only nearly in line with each other, as seen from 
the earth. In the second ease they are really near each other. 
In the ease of stars that are only optically double, it gen- 
erally happens that we can, alter some years, detect their 
mutual independence in the fact that their relative motion is 

in a straight line and uniform. This is a simple consequence 
of the combination of their independent "proper motions." 




Fig. 113. — Double and Multiple Stars. 

If they are physically connected, we find on the contrary that 
the relative motion is in a concave curve; i.e., taking one of 
them as a. centre, the other moves around it. The doctrine of 
chances shows, what direct observation confirms, that tin 1 
Optical pairs must be comparatively rare, and that tin 1 great 
majority of double stars must be really physically connected, 



§ 402] BINARY STARS. 335 

— probably by the same attraction of gravitation which con- 
trols the solar system. 

463. Binary Stars. — Stars thus physically connected are 
also known as binary stars. They revolve in elliptical orbits 
around their common centre of gravity in periods which range 
from 14 years to 1500 (so far as at present known), while the 
apparent major axis of the ovals ranges from 40" to 0".5. The 
elder Herschel, a little more than a century ago, first discovered 
this orbital motion of " binaries " in trying to ascertain the 
parallax of some of the few double stars known at his time. 
It was then supposed that they were simply "optical pairs/' 
and he expected to detect an annual displacement of one of 
the stars with reference to the other. He failed in this, but 
found instead a true orbital motion. 

At present the number of pairs in which this kind of motion has 
been certainly detected is about 200, and is continually increasing as 
our study of the double stars goes on. Most of the double stars have 
been discovered too recently to show any sensible motion as yet, but 
about fifty pairs have progressed so far, either having completed an 
entire revolution or a large part of one, that it is possible to compute 
their orbits with some accuracy. 

464. Orbits of Binaries. — In the case of a binary pair the 
apparent orbit of the smaller star with reference to the larger 
is always an ellipse ; but this apparent orbit is only the true 
orbit seen more or less obliquely. If we assume what is prob- 
able, 1 though certainly not proved as yet, that the orbital motion 
of the pair is under the law of gravitation, we know that the 



1 As has been often pointed out, the question can be decided by spec- 
troscopic observations whenever we become able to observe separately the 
two spectra of the components of a binary and so can determine the radial 
velocity of each at several different points in the orbit. The difficulties 
are great, but probably not insurmountable. 



336 



ORBITS OF BINARIES. 



[§464 



larger star must be in the focus of the true relative orbit 
described by the smaller ; and, moreover, that the latter must 
describe around it equal areas in equal times. By the help of 
these principles, we can deduce from the apparent oval the true 
orbital ellipse ; but the calculation is troublesome and delicate. 

The relative orbit is all that can be determined from micrometer 
observations of the distance and position angle measured between the 
two stars. 




1822 



1718 1885 °° 
7 Virglnis. 



18-S7, 



1878 



500 ± Years. 



180° 



JP 



58 Years. 
1878 
90< 

J Cancri. 



^-^1878 
H-^1827 ■ 




£ Ursoe Majoris 




1750 



Fig. 114. — Orbits of Binary Stars. 



Fig. 114 represents the orbits of four of the best determined double- 
star systems. 

In but a few cases, where we have sufficient meridian-circle obser- 
vations, or where the two components of the pair have had their 
position and distance measured from a neighboring star not partak- 
ing of their motion, we can deduce the absolute motion of each of the 
two stars separately with respect to their common centre of gravity, 
and thus get data for determining their relative masses (Art. 466). 
The case of Sirius is in point. Nearly 40 years ago it had been found 



[§464 



SIZE OF THE ORBITS. 



337 



from meridian-circle observations to be moving for no assignable 
reason in a small oval orbit with a period of about 50 years. In 
1862, Clark found near it a minute companion, which explained 
everything ; only we have to admit that this faint acolyte, which does 
not give T 2tro"o as mucn light as Sirius itself, has a mass more than 
a quarter part as great ; it seems to be one of Bessel's " dark stars." 
Fig. 114* shows the absolute and relative orbits of the system of 
Sirius. 




*■*. Relative Orbit^^- 



Fig. 114*. — Orbit of Sirius. 



The dotted line represents the relative orbit of the companion with 
respect to Sirius, w 7 hile the larger, full-line ellipse is its actual orbit 
around the common centre of gravity, C ; the smaller oval being the 
orbit of Sirius itself around C, as given by meridian-circle observation. 



465. Size of the Orbits. — The real dimensions of a jiouble- 
star orbit can be obtained only when we know its distance 
from us. Fortunately, a number of the stars whose parallaxes 
have been ascertained are also binary, and assuming the best 
available data as to parallax and orbit, we find the following re- 
sults, — the semi-major axis in astronomical units being always 



338 



MASSES OF BINARY STARS. 



[§ 465 



equal to the fraction — , in which a" is the semi-major axis of 
the double-star orbit in seconds of arc, andy is its parallax. 



Name. 


Assumed 
Parallax. 


Angular 
Semi-axis. 


Real 
Semi-axis. 


Period. 


Mass. 
0=1. 


77 Cassiopeise . . 
Sirius .... 
a Centauri . . . 
70 Ophiuchi . . 


0".35 
.39 
.75 
.25 ? 


8".21 

8 .03 

17 .70 

4 .55 


23.5 
20.6 
23.6 
18.2 


195>\8 
52 .2 
81 .1 
88 .4 


0.33 
3.24 

2.00 
0.77 



These double-star orbits are evidently comparable in mag- 
nitude with the larger orbits of the planetary system, none of 
those given being smaller than the orbit of Uranus, and none 
twice as large as that of Neptune. The elements of the orbits 
are from the data of Dr. See. Observations since the reappear- 
ance of the companion in 1897 indicate that the true period of 
Sirius is a little shorter than here given, and its mass there- 
fore somewhat larger. 



465*. Spectroscopic Binaries. — One of the most interesting 
of recent astronomical results is the detection by the spectroscope 
of several pairs of double stars so close that no telescope can separate 
them. In 1889 the brighter component of the well-known double 
star Mizar (Zeta Ursae Majoris, Fig. 113) was found by Pickering to 
show the dark lines double in the photographs of its spectrum, at reg- 
ular intervals of about 52 days. The obvious explanation is that this 
star is composed of two, which revolve around their common centre 
of gravity, in an orbit whose plane is nearly edgewise towards us. 
When the stars are at right angles to the line along which we view 
them, one of them will be moving towards us, the other from us, and 
as a consequence, according to Doppler's principle (Arts. 200 and 500), 
the lines in their spectra will be shifted opposite ways. Now since 
the two stars are so close that their spectra overlie each other, the 
result will be simply to make the lines in the compound spectrum 
apparently double. From the distance between the two components 
of the lines thus doubled, the relative velocity of the two stars can be 



[§ 465* SPECTROSCOPIC BINARIES. 339 

found ; and from this (knowing the period) the size of the orbit and 
the united mass of the stars. Thus it appears that in the case of 
Mizar, the relative velocity of the two components is about 100 miles 
a second, the period 104 days, and the distance between the two stars 
about 140 millions of miles ; from which it follows (Art. 466) that 
the united mass of the two is about 40 times that of the sun. 

The lines in the spectrum of Beta Aurigae exhibit the same pecu- 
liarity, but the doubling occurs once in four days. The relative 
velocity is about 150 miles a second, and the diameter of the orbit 
about 8,000000 miles, the united mass of the pair being about two 
and a half times that of the sun. 

In 1896 two other similar cases were announced by Professor 
Pickering, discovered on the South American spectrum photographs. 
The first is Mu x Scorpii, with a period of 34 h 42.5 m : the size of the 
orbit not then determined. The second is 3105 Lacaille in Puppis, 
with a period of 74 h 46 m . In both cases the components are consid- 
erably unequal. 

These observations were all made by photographing the spectrum 
with the slitless spectroscope (Art. 458), and are only possible in cases 
where the stars which compose the pair are both reasonably bright. 

With his slit-spectroscope, Yogel, as has already been stated in the 
preceding article, detected about the same time a similar orbital motion 
in Algol, although the companion of the brighter star does not give 
light enough to form a spectrum of its own. 

A year later he found another similar result in the case of the bright 
star Alpha Virginis (Spica). The star is really double, having a 
small companion like that of Algol, not bright enough to make a 
perceptible spectrum, but heavy enough to make its partner swing 
around in an orbit 6,000000 miles in diameter once in four days. 
The sun is not quite in the plane of the orbit, so that Spica is never, 
like Algol, eclipsed by its attendant. 

In 1895-6, Belopolsky of Pulkowa found by the same method that 
the brighter component of the double star Castor has a companion 
like that of Spica, producing an orbital motion with a period of 3 days 
and a speed of about 15.5 miles a second. He has also obtained 
spectroscopic evidence that the variable star Delta Cephei has an 
orbital velocity of about 13 miles a second. Lockyer has announced 
similar results as to the variables Eta Aquilaa, Zeta Geminorum, 
T. Vulpeculse, and S. Sagittae ; but as yet without details. Beta 



340 PLANETARY SYSTEMS ATTENDING STARS. [§ 465* 

Lyra? also, in all probability, is to be counted in the same class. The 
lines of its spectrum double as well as shift. 

466. Masses of Binary Stars. —If we assume that the 
binary stars move under the law of gravitation, then when w r e 
know the semi-major axis of the orbit in astronomical units 
and the period of revolution, we can find the mass of the pair 
as compared with the sun by the proportion (Art. 309) 

S + e:M+m::l:- 2 , 

in which S + e is the united mass of the sun and earth (e is 
insignificant), M + m is the united mass of the two stars, a 
the semi-major axis of their orbit in astronomical units, and 
t their period in years. This gives 

The final column of the little table gives the masses of the star- 
pairs resulting from the data which are presented ; but the reader must 
bear in mind that they are not much to be relied on, because of the 
uncertainty of the parallaxes in question. A slight error in the paral- 
lax makes a vastly greater error in the resulting mass. The reader is 
also reminded of the fact that the mass of the pair gives no clue to 
the diameter or density of the stars. 

466*. Evolution of Binary Systems. — As already remarked 
(Art. 462) the theory of probabilities indicates that the great 
majority of double stars must be physically connected, but our 
observations have not yet continued long enough to give us 
anything like an accurate knowledge of the orbits of more than 
a very few. Table VII (Appendix) presents a list of twenty, 
mostly computed by Dr. See, which may be regarded as fairly 
known. Two others of long period are added, not yet, how- 
ever, to be accepted as reliable, the data being insufficient. 

It will be noticed that the orbits are very eccentric as com- 
pared with those of the planets, the average eccentricity of 
the stellar orbits being nearly 0.50. Dr. See has investigated 
the probable origin of these binary systems, and finds that 



§ m] PLANETARY SYSTEMS ATTENDING STARS. 341 

all the peculiarities of their orbits can be accounted for by the 
theory of " tidal evolution 7 ' (Art. 281). It is supposed that 
in such cases the primitive nebula as it whirls assumes the 
dumb-bell form known as the " apioid " : the two parts separ- 
ate, and as they revolve around their common centre of gravity 
great tides are raised, which by their interaction push the 
spinning globes apart into eccentric orbits. 

467. Planetary Systems attending Stars. — It is a natural 

question whether some, at least, of the stars have not planetary systems 
of their own, and whether some of the small " companions " that we 
see may uot be the Jupiters of such systems. We can only say as to 
this that no telescope ever constructed could even come near to making- 
visible a planet which bears to its primary approximately the relations 
of size, distance, and brightness which Jupiter bears to the sun. In the 
solar system, viewed from our nearest neighbor among the stars, Jupi- 
ter would be a star of about the twenty-first magnitude, not quite 5" 
distant from the sun, which itself would be a star of the second magni- 
tude. To render a star of the twenty-first magnitude barely visible 
(apart from all the difficulties raised by the proximity of a larger star) 
would require a telescope of more than 20 feet aperture. 

468. Multiple Stars. — There are a considerable number of 
cases where we find three or more stars connected in one sys- 
tem. Zeta Cancri consists of a close pair revolving in a nearly 
circular orbit, with a period of somewhat less than 60 years, 
while a third star revolves in the same direction around them, 
at a much greater distance, and with a period that must be at 
least 500 years. Moreover, the third star is subject to a pecu- 
liar irregularity in its motion, which seems to indicate that it 
has an invisible companion very near it, the system probably 
being really quadruple. In Epsilon Lyrse we have a most 
beautiful quadruple system composed of two pairs, each pair 
making its own slow revolution with a period of over 200 
years ; probably, moreover, since they have a common proper 
motion, the two pairs revolve around each other in a period 
only to be reckoned by milleniums. In Theta Orionis we have 



342 



CLUSTERS. 



[§468 



a multiple star in which the six components are not organized 
in pairs, but are at not very unequal distances from each other 
(see Fig. 113). 

469. Clusters. — There are in the sky numerous groups of 
stars, containing from a hundred to many thousand members. 
A few are resolvable by the naked eye, as, for instance, the 







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Fig. 115. — The Pleiades. 



Pleiades (Fig. 115) ; some, like "Prsesepe " (in Cancer), break 
up under the power of even an opera-glass ; but most of them 
require a large telescope to show the separate components. 



§ 469] NEBULAE. 343 

To the naked eye or small telescopes, if visible at all, they 
look merely like faint clouds of shining haze ; but in a large 
telescope they are among the most magnificent objects the 
heavens afford. The cluster known as " 13 Messier," not far 
from the " apex of the sun's way," is perhaps the finest. 

The question at once arises whether the stars in such a 
cluster are comparable with our own sun in magnitude, and 
separated from each other by distances like that between the 
sun and Alpha Centauri, or whether they are really small and 
closely packed, — mere sparks of stellar matter, — whether 
the swarm is about the same distance from us as the stars, or 
far beyond them. Forty years ago the prevalent view was 
that these clusters are stellar universes, — " galaxies," like the 
group of stars to which it was supposed the sun belongs, — 
but so inconceivably remote that in appearance they dwindle 
to mere shreds of luminous cloud. It is now, however, quite 
certain that the opposite view is correct. The star clusters 
are among our stars, and form a part of our own stellar uni- 
verse. Large and small stars are so associated in the same 
cluster as to leave no doubt, although it has not yet been 
possible to determine the actual parallax and distance of any 
cluster. 

NEBULAE. 

470. Besides the luminous clouds which under the telescope 
break up into separate stars, there are others which no tele- 
scopic power resolves, and among them some which are 
brighter than many of the clusters. These irresolvable objects, 
which now number something like 8000, are "the nebulae." 
Two or three of them are visible to the naked eye, — one, the 
brightest of all, and the one in which the temporary star 
of 1885 appeared, is in the constellation of Andromeda, and is 
represented in Fig. 116 as seen in a good-sized telescope. 
Another most conspicuous and very beautiful nebula is that in 
the sword of Orion. 



344 



NEBULAE. 



[§470 



The larger and brighter nebulae are mostly irregular in form, 
sending out sprays and streams in all directions, and contain- 
ing dark openings and " lanes." Some of them are of enor- 
mous volume. The nebula of Orion (which includes within 
its boundary the multiple star Theta Orionis) covers several 
square degrees, and since we know with certainty that it is 
more remote than Alpha Centauri, its cross-section as seen 

from the earth must ex- 
ceed the area of Nep- 
tune's orbit by many 
thousand times. The 
nebula of Andromeda is 
not quite so extensive, 
and it is rather more 
regular in its form. The 
smaller nebulae are, for 
the most part, more or 
less nearly oval in form 
and brighter in the cen- 
tre. In the so-called 
" nebulous stars," the 
central nucleus is like a 
star shining through a 
fog. The " planetary 
nebulae" are nearly cir- 
cular and of about uni- 
form brightness through- 
out, and the rare " annular or ring nebulae " are darker in the 
centre. Fig. 117 is a representation of the finest of these 
ring-nebulae, that in the constellation of Lyra. There are a 
number of nebulae which exhibit a remarkable spiral structure 
in large telescopes. There are several double nebulae, and a 
few that are variable in brightness, though no periodicity has 
yet been ascertained in their variations. 

The great majority of the eight thousand nebulae are ex- 




Fig. 116. 
Telescopic View of the Great Nebula in Andromeda. 



470] 



DRAWINGS AND PHOTOGRAPHS. 



345 



tremely faint, but the few that are reasonably bright are very 
interesting objects. 



471. Drawings and Photographs of Nebulae. — Not very long 
ago the correct representation of a nebula was an extremely dif- 
ficult task. A few more or less elaborate engravings exist of 
perhaps fifty of the most conspicuous of them ; but photogra- 
phy has recently taken possession of the field. The first suc- 
cess in this line was by Henry Draper of New York, in 1880, 
in photographing the nebula of Orion. Since his death in 
1882, great progress has 
been made, both in Eu- 
rope and this country, 
and at present the pho- 
tographs are continually 
bringing out new and 
before unsuspected fea- 
tures. Fig. 118, for in- 
stance, is from a photo- 
graph of the nebula of 
Andromeda, taken by 
Mr. Eoberts of Liverpool 
in December, 1888, and 
shows that the so-called 
" dark lanes," which hith- 
erto had been seen only 
as straight and wholly 
inexplicable markings, as 
represented in Fig. 116, 
are really curved ovals, like the divisions in Saturn's rings. 
The photograph brings out clearly a distinct annular struc- 
ture pervading the whole nebula, though as yet not satisfac- 
torily seen by the eye with any telescope. 

The photographs not only show new features in old nebulae, 
but they reveal numbers of new nebulae invisible to the eye 
with any telescope. 




Fig. 117. — The Annular Nebula in Lyra. 



346 



PHOTOGRAPHS OF NEBULAE. 



[§471 



Thus, in the Pleiades, it has been found that nearly all the larger 
stars have wisps of nebulous matter attached to them, as indicated by 
the dotted outlines in Fig. 115 : and in a small territory in and near 




Fig. 118. -— Mr. Roberts's Photograph of the Nebula of Andromeda. 

the constellation of Orion, Pickering, with an eight-inch photographic 
telescope, found upon his star plates nearly as large a number of 



§ 471 J CHANGES IN NEBULAE. 347 

new nebulae as of those that were previously known within the same 
boundary. 

The photographs of nebulas require, generally, an exposure of from 
one hour to four or five, or even more. The images of all the brighter 
stars in the field are therefore enormously over-exposed, and seriously 
injure the picture from an artistic point of view. 

472. Changes in Nebulae. — It cannot perhaps be stated with 
certainty that sensible changes have occurred in any of the nebulas, 
since they first began to be observed, — the early instruments were so 
inferior to the modern ones that the older drawings cannot be trusted 
very far ; but some of the differences between the older and more re- 
cent representations make it extremely probable that real changes are 
going on. Probably after a reasonable interval of time, photography 
will settle the question. 

473. Spectra of Nebulae. — One of the most important of 
the early achievements of the spectroscope was the proof that 
the light of the nebulae proceeds not from aggregations of 
stars, but from glowing gas in a condition of no great density. 
Huggins, in 1864, first made the decisive observation by finding 
bright lines in their spectra. 

So far the spectra of all the nebulae that show lines at all 
appear to be substantially the same. Four lines are usually 
easily observed; two of which are due to hydrogen ; but the 
other two, which are brighter than the hydrogen lines, are not 
yet identified, and are almost certainly due to some element 
not yet detected on the earth or sun, and are apparently peculiar 
to the nebulae. At one time the brightest of the four lines 
was thought to be due to nitrogen, and even yet the statement 
that this is the case is found in many books ; but it is now 
certain that whatever it may be, nitrogen is not the substance. 

Mr. Lockyer has ascribed this line to magnesium in connection with 
his " meteoric hypothesis " ; but elaborate observations of Huggins 
and others show conclusively that this identification also is incorrect. 

Fig. 119 shows the position of the principal lines so far observed : 
in the brighter nebulas a number of others are also sometimes seen, 



348 DISTANCE AND DISTKIBUTlON OF NEBULA. [§ 473 

and over seventy lines have been photographed in the spectra of differ- 
ent nebulae : the lines of helium are generally found to be present. 
One of Mr. Huggins's photographic spectra of the nebula of Orion 
shows, in addition to those that are visible to the eye, a considerable 
number of bright lines in the ultra-violet ; and, what is interesting, 
these lines seem to pertain also to the spectrum of the stars in the 
so-called "Trapezium" (Theta Ononis), as if, which is very likely, 
the stars themselves were mere condensations of the nebulous matter. 




Fig. 119. — Spectrum of the Gaseous Nebulae. 

ISTot all nebulae show the bright-line spectrum. Those which 
do — about half the whole number — are of a greenish tint, 
at once, recognizable in. a large telescope. The white nebulae, 
with the nebula of Andromeda, the brightest of all, at their 
head, present only a plain, continuous spectrum, unmarked by 
lines of any kind. This, however, does not indicate neces- 
sarily that the luminous matter is not gaseous, for a gas 
under pressure gives a continuous spectrum, like an incan- 
descent solid or liquid. The telescopic evidence as to the non- 
stellar constitution of nebulae is the same for all : no nebula 
resists all attempts at resolution more stubbornly than that 
of Andromeda. 

Keeler at the Lick Observatory has very recently observed a num- 
ber of the brighter nebula with a spectroscope of high dispersive 
powers, and has been able to detect and to measure the motion of 
several of them along the line of sight. The velocity of their motion 
appears to be of the same order as that of the stars, the nebulae ob- 
served giving results ranging from zero up to about 40 miles a second 
— some approaching and others receding. The nebula of Orion is 
receding at the rate of about ten miles a second. 



§ 474 3 THE SIDEREAL HEAVENS. 349 

As to the real constitution of these bodies, we can only 
speculate. The fact that the matter which shines is mainly 
gaseous does not make it certain that they do not also contain 
dark matter, either liquid or solid. What proportion of it 
there may be we have at present no means of knowing. 

474. Distance and Distribution of Nebulae. — As to their 
distance, we can only say that, like the star-clusters, they are 
within the stellar universe, and not beyond its boundaries, as 
is clearly shown by the nebulous stars first pointed out and 
discussed by the older Herschel, and by such peculiar associa- 
tion of stars and nebulae as we find in the Pleiades. 

Moreover, in certain curious luminous masses known as the 
"Nubeculse" (near the south pole), we have stars, star-clus- 
ters, and nebulae intermingled promiscuously. 

In the sky generally, however, the distribution of the nebulae 
is in contrast with that of the stars. The stars crowd together 
near the Milky Way : the nebulae, on the other hand, are most 
numerous just where the stars are fewest, as if the stars had 
somehow consumed in their formation the substance of which 
the nebulae are made ; or as if, possibly, on the other hand, 
the nebulae had been formed by the disintegration of stars, 
as a few astronomers have maintained, in opposition to the 
more common view. 

THE CONSTITUTION OF THE SIDEREAL HEAVENS. 

475. The Galaxy or Milky Way. — This is a luminous belt 
of irregular width and outline, which surrounds the heavens 
nearly in a great circle. It is very different in brightness in 
different parts, and in several constellations it is marked by 
dark bars and patches which make the impression of overlying 
clouds : the most notable of them is the so-called " Coal-sack," 
near the southern pole. For about a third of its length (from 
Cygnus to Scorpio) it is divided into two roughly parallel 
streams. The telescope shows it to be made up almost wholly 



350 



DISTRIBUTION OF THE STARS. 



[§476 



of small stars, from the eighth magnitude down ; it contains 
also numerous star-clusters, but very few true nebulae. 

The galaxy intersects the ecliptic at two opposite points 
not far from the Solstices, and at an angle of nearly 60°, its 
" northern pole " being, according to Herschel, in the constel- 
lation of Coma Berenicis. 

As Herschel remarks, "the 'galactic plane' is to the sidereal 
universe much what the plane of the ecliptic is to the solar 
system, — a plane of ultimate reference, and the ground plan 
of the stellar system." 

476. Distribution of the Stars in the Heavens. — It is obvious 
that the distribution of the stars is not even approximately 
uniform : they gather everywhere in groups and streams. But 
besides this the examination of any of the great star-catalogues 
shows that the average number to a square degree increases 
rapidly and pretty regularly from the galactic pole to the 
galactic circle itself, where they are most thickly packed. 
This is best shown by the "star-gauges " of the elder Herschel, 
each of which consisted merely in an enumeration of the stars 
visible in a single field of view of his 20-foot reflector, the 
field being 15' in diameter. 

He made 3400 of these " gauges," and his son followed up the work 
at the Cape of Good Hope with 2300 more in the south circumpolar 
regions. From the data of these star-gauges, Struve has deduced the 
following figures for the number of stars visible in one field of view : 



Distance from Galactic Circle. 


Average No. of Stars in Field 


90° 


4.15 


75° 




4.68 


60° 




6.52 


45° 




10.36 


30° 




17.68 


15° 




30.30 







122.00 



477. Structure of the Stellar Universe. — Herschel, starting 



§ *'?] DO THE STARS FORM A SYSTEM ? 351 

from the unsound assumption that the stars are all of about 
the same size and brightness, and separated by approximately 
equal distances, drew from his observations certain untenable 
conclusions as to the form and structure of the " galactic clus- 
ter/' to which the sun was supposed to belong, — theories for 
a time widely accepted and even yet more or less current, 
though in many points certainly incorrect. 

But although the apparent brightness of the stars does not 
thus depend mainly upon their distance, it is certain that, as a 
class, the faint stars are smaller, darker, and more remote than 
the brighter ones ; we may, therefore, safely draw a few con- 
clusions, which, so far as they go, substantially agree with 
those of Herschel. 

478. I. The great majority of the stars we see are con- 
tained within a space having roughly the form of a rather 
thin, flat disc, with a diameter eight or ten times as great as 
its thickness, our sun being not very far from its centre. 

II. Within this space the naked-eye stars are distributed 
rather uniformly, but with some tendency to cluster, as shown 
in the Pleiades. The smaller stars, on the other- hand, are 
strongly " gregarious," and are largely gathered in groups and 
streams, which have comparatively vacant spaces between them. 

III. At right angles to the " galactic plane n the stars are 
scattered more evenly and thinly than in it, and we find here 
on the sides of the disc the comparatively starless region of 
the nebulae. 

IV. As to the Milky Way itself, it is not certain whether 
the stars which compose it form a sort of thin, flat, continuous 
sheet, or whether they are ranged in a kind of ring, with a com- 
paratively empty space in the middle where the sun is placed. 

As to the size of the disc-like space which contains most of 
the stars, very little can be said positively. Its diameter must 
be as great as 20,000 or 30,000 light years, — how much greater 
we cannot even guess ; and as to " the beyond " we are still 
more ignorant. If, however, there are other stellar systems 



352 COSMOGONY. [§ 479 

of the same order as our own, these systems are neither the 
nebulae nor the clusters which the telescope reveals, but are 
far beyond the reach of any instrument at present existing. 

479. Do the Stars form a System? — It is probable that 
gravitation 1 operates between the stars (as indicated by the 
motions of the binaries), and they are certainly moving very 
swiftly in various directions. The question is whether these 
motions are governed by gravitation, and are " orbital " in the 
ordinary sense of the word. 

There has been a very persistent belief that somewhere 
there is u a great central sun," around which the stars are all 
circling. As to this, there is no longer any question — the 
" central sun " speculation is certainly unfounded, though we 
have not space for the demonstration of its fallacy. 

Another less improbable doctrine is that there is a general revolu- 
tion of the mass of stars around the centre of gravity of the whole, a 
revolution nearly in the plane of the Milky Way. Some years ago, 
Maedler, in his speculations, concluded that this centre of gravity of 
the stellar universe was not far from Alcyone, the brightest of the 
Pleiades, and that therefore this star was in a sense the "central sun. ,, 
The evidence, however, is entirely inconclusive, nor is there yet proof 
of any such general revolution. 

480. On the whole, the most probable view seems to be that 
the stars are moving much as bees do in a swarm, each star 
mainly under the control of the attraction of its nearest neigh- 
bors, though influenced more or less, of course, by that of the 
general mass. If so, the paths of the stars are not " orbits " 
in any periodic sense ; i.e., they are not paths which return 
into themselves. The forces which at any moment act upon a 
given star are so nearly balanced that its motion must be 
sensibly rectilinear for thousands of years at a time. 

1 It must be remembered, however, that Hall and others have shown 
that the motion of the binaries does not absolutely prove the operation of 
gravitation. 



§ 481 J THE PLANETARY SYSTEM. 353 

The solar system is an absolute despotism, the sun being 
dominant and supreme. In the stellar system, on the other 
hand, there is no such central power : it is a pure democracy, 
in which the individuals are governed by their neighbors, and 
by the authority of the whole community to which they them- 
selves belong. 

481. Cosmogony. — One of the most interesting and one of 
the most baffling topics of speculation relates to the process 
by which the present state of things has come about. In a 
forest, to use an old comparison of HerscheFs, we see around 
lis trees in all stages of their life history, from the sprouting 
seedlings to the prostrate and decaying trunks of the dead. Is 
the analogy applicable to the heavens, and if so which of 
the heavenly bodies are in their infancy, and which decrepit 
with age ? 

At present many of these questions seem to be absolutely 
beyond the reach of investigation even. Others, though at 
present unsolved, appear approachable, and a few we can 
already answer. In a general way we may say that the con- 
densation of diffuse, cloud-like masses of matter under the 
force of gravitation, the conversion into heat of the energy 
of motion and of position (the " kinetic" and "potential" 
energy -*— Physics, p. 121) of the particles thus concentrated/ 
the effect of this heat upon the mass itself, and the effect of 
its radiation upon surrounding bodies, — these principles cover 
nearly all the explanations that can thus far be given of the 
present condition of the heavenly bodies. 

482. Genesis of the Planetary System. — Our planetary sys- 
tem is clearly no accidental aggregation of bodies. Masses of 
matter coming haphazard to the sun would move (as the comets 
actually do move) in orbits which, though always conic sec- 
tions, would have every degree of eccentricity and inclination. 
In the planetary system this is not so. Numerous relations 



354 THE NEBULAR HYPOTHESIS, [§ *82 

exist for which the mind demands an explanation, and for 
which gravitation does not account. 

We note the following as the principal : — 
1. The orbits of the planets are all nearly circular. 
2o They are all nearly in one plane (excepting those of some of the 
asteroids). 

3. The revolution of all, without exception, is in the same direction. 

4. There is a curious and regular progression of distances (expressed 
by Bode's Law; which, however, breaks down with Neptune). 

As regards the planets themselves : — 

5. The plane of the planet's rotation nearly coincides with that of 
the orbit (probably excepting Uranus). 

6. The direction of rotation is the same as that of the orbital revo- 
lution (excepting probably Uranus and Neptune). 

7. The plane of the orbital revolution of the planet's satellites 
coincides nearly with that of the planet's rotation, wherever this can 
be ascertained. 

8. The direction of the satellites' revolution also coincides with 
that of the planet's rotation (with the same limitation). 

9. The largest planets rotate most swiftly. 

Now this arrangement is certainly an admirable one for a 
planetary system, and therefore some have argued that the 
Deity constructed the system in that way, perfect from the first. 
But to one who considers the way in which other perfect works 
of nature usually attain to their perfection, — their processes 
of growth and development, — this explanation seems improb- 
able. It appears far more likely that the planetary system 
was formed by growth than that it was built outright. 

483. The Nebular Hypothesis. — The theory which in its 
main features is now generally accepted, as supplying an in- 
telligible explanation of the facts, is that known as "the neb- 
ular hypothesis. " In a more or less crude and unscientific 
form, it was first suggested by Swedenborg and Kant, and after- 
wards, about the beginning of the present century, was worked 
out in mathematical detail by La Place. He maintained — 



§ 483 1 THE NEBULAR HYPOTHESIS. 355 

(a) That at some time in the past 1 the matter which is now 
gathered into the sun and planets was in the form of a nebula. 

(b) This nebula, according to him, was a cloud of intensely 
heated gas. (As will be seen, this postulate is questionable.) 

(c) Under the action of its own gravitation, the nebula as- 
sumed a form approximately globular, with a motion of rotation, 
the rotational motion depending upon accidental differences in 
the original velocities and densities of different parts of the 
nebula. As the contraction proceeded, the swiftness of the 
rotation would necessarily increase for mechanical reasons : 
since every shrinkage of a revolving mass implies a shortening 
of its rotation period. 

(d) In consequence of the rotation, the globe would neces- 
sarily become flattened at the poles, and ultimately, as the 
contraction went on, the centrifugal force at the equator would 
become equal to gravity, and rings of nebulous matter, like the 
rings of Saturn, would be detached from the central mass. In 
fact, Saturn's rings suggested this feature of the theory. 

(e) The ring thus formed would for a time revolve as a 
whole, but would ultimately break, and the material would col- 
lect into a globe revolving around the central nebula as a planet. 2 
La Place supposed that the ring would revolve as if solid, the 
particles at the outer edge moving more swiftly than those at 
the inner. If this were always so, the planet formed would 
necessarily rotate in the same direction as the ring had revolved. 

(/) The planet thus formed might throw off rings of its 
own, and so form for itself a system of satellites. 

1 As to the origin of the nebula itself, he did not speculate. There wat 
no assumption, as is often supposed, that matter was first created in the 
nebulous condition. It was only assumed that, as the egg may be taken 
as the starting-point for the life history of an animal, so the nebula is to 
be regarded as the starting-point of the life history of the planetary system. 

2 It has been suggested by Huggins and others that the small nebulae 
near the great nebula of Andromeda (see Fig. 118) may be "planets" in 
process of formation. 



35G lockyer's meteoric hypothesis. [§ 4y3 

The theory obviously explains most of the facts of the so- 
lar system, which were enumerated in the preceding article, 
though some of the exceptional facts, such as the short periods 
of the satellites of Mars, and the retrograde motions of those 
of Uranus and Neptune, cannot be explained by it alone in its 
original form. Even they, however, do not contradict it, as is 
sometimes supposed. 

Many things also make it questionable whether the outer plan- 
ets are so much older than the inner ones, as the theory would 
indicate. It is not impossible that they may even be younger. 

484. On the whole, we may say that while in its main out- 
lines the theory probably is true, it also probably needs serious 
modifications in details. It is rather more likely, for instance, 
that the original nebula was a cloud of ice-cold meteoric dust 
than an incandescent gas, or a "fire-mist," to use a favorite ex- 
pression; and it is likely that planets and satellites were often 
separated from the mother-orb otherwise than in the form of 
rings. Nor' is it possible that a thin, wide ring could revolve 
in the same way as a solid, coherent mass : the particles near 
the inner edge must make their revolution in periods much 
shorter than those upon the circumference. 

A most serious difficulty arises also from the apparently 
irreconcilable conflict between the conclusions as to the age 
and duration of the system, which are based on the theory of 
heat (see Art. 489) and the length of time which would seem 
to be required by the nebular hypothesis for the evolution of 
our system. 

Our limits do not permit us to enter into a discussion of Darwin's 
" tidal theory" of satellite formation, which may be regarded as in a 
sense supplementary to the nebular hypothesis ; nor can we more than 
mention Faye's proposed modification of it. According to him, the 
inner planets are the oldest. 

485. Lockyer's Meteoric Hypothesis. — Within the last few 
years, Mr. Lockyer has vigorously revived a theory which has 



§ 485] STARS, STAR-CLUSTERS, AND NEBULAE. 357 

been from time to time suggested before ; viz., That all the heav- 
enly bodies in their present state are mere clouds of meteors, 
or have been formed by the aggregation of such clouds : and 
it is an interesting fact, as G. H. Darwin has recently shown, 
that a large swarm of meteors in which the individuals move 
swiftly in all directions would, in the long run, and as a tvJiole, 
behave almost exactly, from a mechanical point of view, in 
the same way as one of La Place's " gaseous nebulae." 

This is not very strange, after all. According to the modern 
"kinetic theory of gases " (Physics, p. 157), a meteor-cloud is mechan- 
ically just the same thing as a mass of gas magnified. The kinetic 
theory asserts that a gas is only a swarm of minute molecules, the 
peculiar gaseous properties depending upon the collisions of these 
molecules with each other and with the walls of the enclosing vessel. 
Magnify sufficiently the molecules and the distances between them, 
and you have a meteoric cloud. 

The spectroscopic " facts " upon which Mr. Lockyer rests 
his attempted demonstration are, indeed, many of them rather 
doubtful, but that does not really discredit the main idea, ex- 
cept in so far as the question of the origin and nature of the 
light produced is concerned. He makes the light in all cases 
depend upon the collisions between the meteors, and finds in 
the spectra of the heavenly bodies evidences of the presence 
of materials with which we are familiar in the meteorites 
that fall upon the earth's surface. These identifications are 
in many cases questionable, and it seems much more probable 
that the luminosity depends to a great degree upon other than 
mere mechanical actions. 

486. Stars, Star-clusters, and Nebulae. — It is obvious that 
the nebular hypothesis in all of its forms applies to the ex- 
planation of the relations of these different classes of bodies 
to each other. In fact, Herschel, appealing only to the " law 
of continuity," had concluded, before La Place formulated his 
theory, that the nebulae develop sometimes into clusters, some 



358 CONCLUSIONS FROM THE THEORY OF HEAT. [§ 487 

times into double or multiple stars, and sometimes into single 
stars. He showed the existence in the sky of all the inter- 
mediate forms between the nebula and the finished star. For 
a time, about forty years ago, while it was generally believed 
that all the nebulae were nothing but star-clusters, only too re- 
mote to be resolved by existing telescopes, his views fell rather 
into abeyance ; but they regained acceptance in their essential 
features when the spectroscope demonstrated the substantial 
difference between gaseous nebulae and the star-clusters. 

487. Conclusions from the Theory of Heat. — Kant and La 
Place, as Newcomb says, seem to have reached their results by 
reasoning forwards. Modern science comes to very similar con- 
clusions by working backwards from the present state of things. 

Many circumstances go to show that the earth was once 
much hotter than it now is. As we penetrate below the sur- 
face, the temperature rises nearly a degree (Fahrenheit) for 
every 60 feet, indicating a white heat at the depth of a few 
miles only; the earth at present, as Sir William Thomson 
says, " is in the condition of a stone that has been in the fire 
and has cooled at the surface." 

The moon bears apparently on its surface the marks of the 
most intense igneous action, but seems now to be entirely 
chilled. 

The planets, so far as we can make out with the telescope, 
exhibit nothing at variance with the view that they were once 
intensely heated, while many things go to establish it. Jupi- 
ter and Saturn, Uranus and Neptune, do not seem yet to have 
cooled off to anything like the earth's condition. 

488. As to the sun, we have in it a body continuously 
pouring forth an absolutely inconceivable quantity of heat 
without any visible source of supply. As has been explained 

1 Dr. See has recently worked out the theory of the development of a 
binary pair from a nebula, by a process of tidal evolution. (Art. 466*.) 



§ 489] THE PRESENT SYSTEM NOT ETERNAL. 359 

already (Art. 219), the only rational explanation of the facts, 
thus far presented, is that which makes it a huge cloud-mantled 
ball of elastic substance, slowly shrinking under its own cen- 
tral gravity, and thus converting into the kinetic energy of 
heat 1 the potential energy of its particles, as they gradually 
settle towards the centre. A shrinkage of 300 feet a year in 
the sun's diameter (150 feet in its radius) will account for 
the whole annual out-put of radiant heat and light. 

489. Age and Duration of the System. — Looking backward, 
then, and trying to imagine the course of time and of events 
reversed, we see the sun growing larger and larger, until at 
last it has expanded to a huge globe that fills the largest orbit 
of our system. How long ago this may have been, we cannot 
state with certainty. If we could assume that the amount of 
heat yearly radiated by the solar surface had remained con- 
stantly the same through all those ages, and, moreover, that 
all the radiated heat came only from one single source, the 
slow contraction of the solar mass, apart from any considerable 
original capital in the form of a high initial temperature, and 
without any reinforcement of energy from outside sources, — 
if we could assume these pi*emises, it is easy to show that the 
sun's past history must cover about 15,000000 or 20,000000 
years. But such assumptions are at least doubtful; and, if 
we discard them, all that can be said is that the sun's age 
must be greater, and probably many times greater, than the 
limit we have named. 

Looking forward, on the other hand, from the present 
towards the future, it is easy to conclude with certainty that 
if the sun continues its present race of radiation and contrac- 

1 So far we have no decisive evidence whether the sun has passed its 
maximum of temperature or not. Mr. Lockyer thinks its spectrum 
(resembling as it does that of Capella and the stars of the second class) 
proves that it is now on the downward grade and growing cooler; but 
others do not consider the evidence conclusive. 



860 THE PRESENT SYSTEM NOT ETERNAL. [§490 

lion, and receives no subsidies of energy from without, it must 
within 5,000000 or 10,000000 years become so dense that its 
constitution will be radically changed. Its temperature will 
fall and its function as a sun will end. Life on the earth, as 
we know life, will be no longer possible when the sun has 
become a dark, rigid, frozen globe. At least this is the inev- 
itable consequence of what now seems to be the true account 
of the sun's present activity, and the story of its life. 

490. The Present System not Eternal. — One lesson seems 
to be clearly taught: That the present system of stars and 
worlds is not an eternal one. We have before us every- 
where evidence of continuous, irreversible progress from a 
definite beginning towards a, definite end. Scattered particles 
and masses are gathering together and condensing, so that the 
great grow continually larger by capturing and absorbing the 
smaller. At the same time the hot bodies are losing their heat 
and distributing it to the colder ones, so that there is an unre- 
mitting tendency towards a, uniform, and therefore useless, 
temperature throughout, our whole universe: for heat is avail- 
able as energy (i.e., it can do work) only when it can pass from 
a warmer body to a, colder one. The continual warming up of 
cooler bodies at the expense of holier ones always menus a 

loss, therefore, not of energy, for thai is indestructible, but of 

available energy. To use the ordinary technical term, energy 

is continually "dissipated" by the processes which constitute 
and maintain life on the universe. This dissipation of energy 

can have but one ultimate result, that of absolute stagnation 

when the temperature has become everywhere the same. 

If we carry our imagination backwards, we reach "a begin- 
ning of things," which has no intelligible antecedent; if for- 
wards, we come to an end of things in dead stagnation. That 
in some way this end of things will result in a "new heavens 
and a new earth " is, of course, very probable, but science as 
vet, can present no explanation of the method. 



APPENDIX. 



CHAPTER XVI. 

MISCELLANEOUS AND SUPPLEMENTARY. 

celestial latitude and longitude, — corrections 
to an altitude measured at sea. — calculation 
of the local time from a single altitude of the 
sun. — determination of azimuth. — theory of 
the foucault pendulum. — measurement of mass 
independent of gravity. — the equation of time. 
how the spectroscope makes the solar prom- 
inences visible. — the equation of doppler's prin- 
ciple. — areal, linear, and angular velocities. — 
kepler's harmonic law and the law of gravi- 
tation. — CORRECTION TO THE HARMONIC LAW. — 

newton's verification of gravitation by means 
of the moon. — the conic sections. — formula foe 
the mass of a planet. — elements of a planet's 
orbit. — danger from comets. — twilight. 

491. Relation of Celestial Longitude and Latitude to Right 
Ascension and Declination (supplementary to Art. 38). — fn Fig. 
L20 EC represents the ecliptic, and EQ the celestial equator, 
the point E being the vernal equinox. K is the pole of the 
ecliptic, and 7 > that of the equator, KPGQ being an are of 
the solstitial colure, the circle which is perpendicular both 




362 APPENDIX. [§ 491 

to the equator and the ecliptic. Let S be any star. Through 
it draw KL and PR which will be " secondaries " respectively 
to the ecliptic and equator. Then the star's longitude is EL 

or A, and its latitude is SL or /3. 
In the same way the right ascen- 
sion is ER or a, and the declina- 
tion SR or 8. 

When a and 8 are given, to- 
gether with the obliquity of the 
ip ecliptic or the angle CEQ, it is a 
simple problem of spherical trig- 
onometry to find A and /?. In the 
triangle KPS, KP is equal to the 
obliquity of the ecliptic; PS = 
90° - 8 ; KS == 90° - /?; the angle KPS is (90° + a), because 
QPR = QR = (90° - a) ; PKS = CKL = (90° - X). KP is 
always the same 23° 28', and so when any two of the other 
quantities are given the triangle can be solved. 

492. Corrections to an Altitude measured at Sea (supplemen- 
tary to Arts. 67-69). — (1) Correction for " Semi-diameter." Since 
the observer measures with his sextant the altitude, not of 
the centre, but of the lower edge of the sun's disc (technically 
its lower "limb"), it is necessary to add to the measured 
height the sun's angular semi-diameter as given in the almanac. 
This never differs more than 20" from 16'. 

(2) Correction for "Dip" This correction results from the 
fact that the marine observer measures altitudes from the 
visible horizon (Art. 16). The dip is the angle HOB in Fig. 
3, p. 11, and depends upon the observer's height above the sear 
level. Its value is given in a little table contained in every 
work on navigation, but may be approximately calculated by 
the simple formula, — 



Dip (in minutes of arc) = -y/lleight in feet. 
(For demonstration, see " General Astronomy," Art. 81, note.) 



§492] 



CALCULATING THE LOCAL TIME. 



363 



That is, if the eye is 20 feet above the water the dip by the 
formula is V20 minutes, or 4'.47. (The table makes it 4', 20"; 
i.e., 4'.33.) The dip is to be subtracted from the measured 
altitude, because the visible horizon is always below the true 
horizon. 

(3) Refraction. This has already been explained in Art. 
50. The amount of the correction for any observed altitude is 
found from a table given in all works on navigation or prac- 
tical astronomy. Like the dip, the refraction correction must 
always be subtracted from the observed altitude. 



(4) Parallax. The declination of the sun is given in the 
almanac as it would be if seen from the centre of the earth. 
Before we can apply the equation of Art. 51, we must there- 
fore reduce the actually observed altitude to what it would be 
if observed from that point : the needed correction is what is 
called the geocentric (or diurnal) parallax. 
It may be defined as the difference of 
direction between two lines drawn to the 
body, one from the observer, the other 
from the earth's centre : or what comes 
to the same thing, it is the angle at the 
body made by these two lines. In Fig. 
121, where S is the sun, C the earth's 
centre, and the observer, it is the angle 
OSC, which is the difference between the 
observed or "apparent" zenith distance 
ZOS, and the "true" zenith distance ZCS. 

Since ZCS is always smaller than ZOS, the correction for 
parallax always has to be added to the observed altitude. In 
the case of the sun, this correction never exceeds 9". 




Fig. 121. 



493. Method of Calculating the Local Time from the Sun's 
Altitude (supplementary to Arts. 00 and Of)).— In Fig. 122 the 
circle NZM is the meridian, P being the pole, Z the zenith, and 



364 



APPENDIX. 



[§493 



EQ the equator. S is the sun, whose altitude SH has been 
measured. This altitude (properly corrected for semi-diameter, 
dip, refraction, and parallax), and subtracted from 90°, gives 

ZS, the sun's zenith 
distance, as one side of 
the triangle. The sec- 
ond side ZP is the com- 
plement of JVP, which 
is the observer's lati- 
tude. Finally, since 
AS is the declination 
of the sun (given in the 
almanac) the third side 
PS is the complement 
of the declination. We, therefore, know the three sides of the 
spherical triangle, ZPS, and can find either of its angles. The 
angle at P is the one we want, — the sun's hour-angle (Art. 
32) ; i.e., the apparent time. 

The trigonometrical formula ordinarily used in computing it is 




Determination of Time by the Sun's Altitude. 



sin 



hP=^ 



/sin i 



K*+(4>-S)]smirz-(4>-S)l . 
cos<£ cosS 



in which z is the sun's zenith distance, 8 its declination, and cj> the 
latitude of the observer. We may add that the angle PZS is the 
sun's azimuth at the time of the observation. The third angle, ZSP, 
is called the "parallactic angle" for reasons we cannot here stop to 
explain. 

The observation should be made not near noon , but when the sun 
is as near to the prime vertical (Art. 17) as possible, because when the 
angle at Z is nearly 90° any uncertainty in the side PZ (which de- 
pends on the ship's latitude) will produce the least possible error in 
computing the hour-angle. 

The apparent time, corrected for the equation of lime (which 
is given in the almanac), gives the local mean time, and the 



§493] 



THEORY OF THE FOUCAULT PENDULUM. 



365 



difference between this local time and the Greenwich time 
(furnished by the chronometer) is the longitude. 



494. Theory of the Foucault Pendulum (supplementary to Art. 
77). — The approximate theory of the experiment is very 
simple. A pendulum suspended so as to be equally free to 
swing in any plane (unlike the common clock pendulum in 
this freedom), if set up at the pole of the earth would appear to 
shift around in 24 hours. Really in this case the plane of 
vibration remains fixed, ivhile the earth turns under it. 

This can be easily seen by setting up 
upon a table a similar apparatus, con- 
sisting of a ball hung from a frame 
by a thread and then, while the ball 
is swinging, turning the table around 
upon its castors with as little jar as 
possible. The plane of the swing will 
remain unchanged by the motion of the 
table. 

It is easy to see, moreover, that at the 
equator there will be no such tendency 
to shift ; while in any other latitude the 
effect will be intermediate, and the time 
required for the pendulum to complete 
the revolution of its plane will be longer 
than at the pole. The northern edge 
of the floor of a room (in the northern hemisphere) is nearer 
to the axis of the earth than is its southern edge, and there- 
fore is carried more slowly eastward by the earth's rotation. 
Hence the floor must " skew w around continually, like a post- 
age-stamp gummed upon a whirling globe anywhere except at 
the globe's equator. Every line drawn on the floor, therefore, 
continually shifts its direction, and a free pendulum set at 
first to swing on any such line must apparently deviate at the 
same rate in the opposite direction. 




Fig 123. 

Explanation of the Foucault 
Pendulum Experiment. 




366 APPENDIX. [§ 494 

The total amount of this deviation in a day is easily estimated geo- 
metrically. Suppose a parallel of latitude drawn through the place 
where the experiment is made, and a series of tangents drawn at 

points close together on this parallel. All 
these tangents will meet at some point V 
(Fig. 123) which is on the earth's axis pro- 
duced, and taken together they form a cone 
with its point at V. Now if we suppose 
this cone cut down on one side and opened 
up (technically, "developed "), it would give 
us a sector of a circle, as in Fig. 124, 
and the angle of the sector — the unshaded 
angle AVA' of Fig. 124 — would be the 
J3 sum total of the angles between all the 

Fig. 124. — Developed Cone, tangent lines of which the cone is com- 
posed. It is easy to prove that A BA ' = 
360° X sin lat. (see "General Astronomy "). 

In the northern hemisphere the plane of vibration of the 
Foucault pendulum moves round with the hands of a ivatch; 
in the southern, the motion is reversed. 

495. Determination of Azimuth (supplementary to Art. 88). — 
An important problem of practical astronomy, especially in 
geodetic work, is that of finding the true bearing or azimuth of 
a line on the earth's surface. The process is this : — With 
a carefully adjusted theodolite the observer points alternately 
upon the Pole-star and upon a distant signal erected for 
the purpose, the signal being of course such that it can be 
observed at night, — usually it is a small hole in a screen 
with a lantern behind it, looking like a star as seen through 
the observer's telescope. The readings of the circle of the 
theodolite then give directly the angle between the signal and 
the Pole-star at the moment of each observation, and if the 
Pole-star were exactly at the pole, this angle would be the 
azimuth of the signal. In the actual state of the case it is 
necessary to note accurately the sidereal time of each observa- 



§495] 



MEASUREMENT OF MASS. 



367 




tion of the star, and from this its azimuth at that moment can 
easily be calculated, by means of the PZS triangle, Fig. 125. 

In this we know the side PZ, the 
complement of the observer's latitude ; 
also the side PS, which is the comple- 
ment of the star's declination : and 
finally, we know the hour-angle SPZ\ 
which is simply the difference between 
the observed sidereal time at the mo- 
ment of observation and the Pole-star's 
right ascension. Hence we can easily 
compute the angle at Z, which is the 
stains azimuth ; and when the azimuth 
of the star is known, that of the night- 
signal follows at once. The results are N H H f 
most accurate when the Pole-star hap- Fig. 125.— Determination of Azimuth, 
pens to be near one of its " elonga- 
tions," as at S' or S" . Then errors of even several seconds in noting 
the time are practically harmless. 

The azimuth of the night-signal being determined, the ob- 
server measures the next day the horizontal angle between it 
and the object whose azimuth is required. 

496. Measurement of Mass Independent of Gravity (supple- 
mentary to Art. 98). — It is quite possible to measure masses 
without weighing. In Fig. 126 B is a receptacle carried at 
the end of a horizontal arm A, which is itself attached to an 
axis MN, exactly vertical and free to turn on pivots at top 
and bottom. A spiral spring S, like the hair spring of a 
watch, is connected with this axis so that if A is disturbed 
it will oscillate back and forth at a rate which depends upon 
the stiffness of the spring and the total inertia of the ap- 
paratus. If we put into B one standard " pound " (of mass), 
it will vibrate a certain number of times a minute ; if two 
pounds, it will vibrate more sloivly; if three, still more slowly; 
and so on : and this time of vibration can be determined and 



368 



APPENDIX. 



[§496 



tabulated. To determine now the mass of a body X, we have 
only to put it into the receptacle B, set the apparatus vibrat- 
ing, and count the number of swings in a minute. Referring 
to our table, we find what number of " pounds " in B would 

have given the same rate of 
vibration. We know then 
that the "inertia" of X is the 
same as that of this number 
of "pounds/' and therefore 
its mass is the same. 

This determination is inde- 
fB pendent of all considerations 
of weight : the apparatus would 
give the same results on the 
surface of the moon, or on that 
of Jupiter, as on the earth. It 
is obvious, however, that an 
instrument of this sort could 
not compete in accuracy or 
convenience with a well-made balance, because of the friction 
of the pivots, the resistance of the air, etc. We introduce it 
simply to assist in separating in the pupil's mind the idea of 
mass from that of iveigJit. 




Fig. 126. 



DISCUSSION OF THE EQUATION OF TIME. 

(Supplementary to Art. 128.) 

497. Effect of the Eccentricity of the Orbit. — Near perihexion, 

which occurs about Dec. 31st, the sun's eastward motion on the eclip- 
tic is most rapid. At this time, accordingly, the apparent solar days 
exceed the sidereal by more than the average amount, making the 
sun-dial days longer than the mean. The sun-dial will therefore lose 
time at this season, and will continue to do so until the motion of the 
sun falls to its average value, as it will at the end of about three 
months. Then the sun-dial will gain until aphelion ; and at that 
time (if the clock and the sun-dial were started together at perihelion) 



§497] 



EQUATION OF TIME. 



869 



they will once more agree. During the remaining half of the year, 
the action will be reversed ; i.e., for the first three months after aphe- 
lion the sun-dial will gain, and in the next three lose what it had 
gained. Thus, twice a year, so far as the eccentricity of the earth's 
orbit is concerned, the clock and the sun-dial will agree, — at the times 
of perihelion and aphelion, — while half-way between they will differ 
by about eight minutes. The equation of time (so far as due to this 
cause only) is about -f 8 minutes in the spring, and —8 in the autumn. 

498. Effect of the Inclination of the Ecliptic to the Equator. 

— Even if the sun's motion in longitude, i.e., along the ecliptic, were 
uniform, its motion in right ascension would be variable. If the true 
and fictitious suns started together at the vernal equinox, one moving 
uniformly in the ecliptic and the other in the equator, they would indeed 
be together (i.e., have the same 
right ascensions) at the two sol- 
stices and at the other equinox, 
because it is just 180° from 
equinox to equinox, and the sol- 
stices are exactly half-way be- 
tween them; but at any inter- 
mediate points their right ascen- 
sions would differ. This is easily 
seen by taking a celestial globe 
and marking on the ecliptic the 
point m, Fig. 127, 1 half-way be- 
tween the vernal equinox and 
the solstice, and also marking a point n on the equator, 45° from the 
equinox. It will be seen at once that the former point is west of n ; 
so that m in the apparent diurnal revolution of the sky will come 
first to the meridian. In other words, when the smn is half-way 
between the vernal equinox and the summer solstice, the sun-dial, 
so far as the obliquity of the ecliptic is concerned, is faster than the clock, 
and this component of the equation of time is minus. The difference, 
measured by the arc of the equator m' n, amounts to nearly 10 minutes. 
Of course the same thing holds, mutatis mutandis, for the other quadrants. 




Fig 



127. — Effect of Obliquity of Ecliptic 
in producing Equation of Time. 



1 The figure represents a globe seen from the west side, with the vernal 
equinox at E. EC is the eclintio. and EQ the equator. 



370 



APPENDIX. 



[§498 



If the ecliptic be divided into equal portions from E to C, and 
hour-circles be drawn from P through the points of division, it will at 
once be seen that near E the portions of the ecliptic are longer than 
the corresponding portions of the equator, the arc of the ecliptic being 
the hypothenuse of a right-angled triangle which has the arc of the 
equator for its base. On the other hand, near the solstice C, the arc 
of the ecliptic is shorter than the corresponding arc of the equator, on 
account of the divergence of the hour-circles as they recede from the 
pole. 

499. Combination of the Effects of the Two Causes. — We 

can represent the two components of the equation of time and the 
result of their combination by a graphical construction — as follows 
(Fig. 128): - 

The central horizontal line is a scale of dates one year long, the 
letters denoting the beginning of each month. The dotted curve 




Fig. 128. — The Equation of Time. 



shows that component of the equation of time which is due to the 
eccentricity of the earth's orbit (Art. 497). Starting at perihelion 
on Dec. 31st, this component is zero, rising to a value of about + 8 
minutes on April 2d, falling to zero on June 30th, and reaching the 
second maximum of — 8 minutes about October 1st. In the same 
way the broken-line curve denotes the effect of the obliquity of the 
ecliptic (Art. 498), which, alone considered, would produce an equa- 
tion of time having four maxima of approximately ten minutes each, 



§ 499] THE EQUATION OF DOPPLER's PRINCIPLE. 371 

on about the 6th of February, May, August, and November, and 
reducing to zero at the equinoxes and solstices. The full-lined curve 
represents their combined effect, and is constructed by making its 
"ordinate" at each point equal to the sum (algebraic) of the ordinates 
of the two other curves. 



500. The Equation of Doppler's Principle (supplementary to 
Art. 200). If V is the velocity of light (186,330 miles a second), and 
r and s are the velocities with which the observer and luminous ob- 
ject respectively are receding from each other ; then, if L be the nor- 
mal wave-length of a ray, and X 1 its observed wave-length as affected 

by the motions, Doppler's equation is L 1 — Ly-^z ), which holds 

good for all values of r and s. When they are small compared with 
F, as is always practically the case, the equation becomes, very ap- 
proximately, L x — L( ^- -J, or — V= — = — zj—. If the bodies 

are approaching, r and s become negative ; i.e. L x is less than L. A 
ray of wave-length L will therefore be found in the observed spectrum 
ichere a ray of wave-length L x would fall were it not for the motion ; in 
other words, the place of the ray will be shifted in the spectrum. 

The rate at which the distance between the observer and the body 
is increasing is obviously (r -f- s), for which we may put the single 
quantity v, since the observations do not decide what part of the whole 
change of distance is due to the motion of the observer. We then 

have, v — V ( — ^-z — ), which is the formula generally given. 

In this way, with powerful spectroscopes, motions of approach or 
recession along the line of sight can be detected if they amount to 
more than one or two miles a second, but the exact measurement is 
very delicate and difficult, and is embarrassed by the recently discov- 
ered fact that the wave-lengths of the rays from a luminous gas are 
slightly increased by pressure. 

501. How the Spectroscope enables us to see the Chromosphere 
and Prominences without an Eclipse (supplementary to Art. 203). 
— The reason why we cannot see the prominences and chromosphere 
at any time by simply screening off the sun's disc, is the brilliant illumi- 
nation of our own atmosphere. 



372 



APPENDIX. 



[§501 











- - — - _- i 




9 






a 




- 






P=V Y-^ * . 


I 


A 




\ 




llllllfci^'lllli 

m: 


iiiiiiii 





Fig. 129. — Spectroscope Slit ad- 
justed for Observation of the 
Prominences. 



When we point the " telespectroscope " (Art. 194) so that the sun's 
image falls as shown in Fig. 129, with its limb just tangent to the 
edge of the slit, then if there is a prominence at that point we shall 
get two overlying spectra ; one, the spectrum of the air light, the other, 

that of the prominence itself. The latter 
is a spectrum composed of bright lines, or, 
if the slit be opened a little, of bright 
images of whatever part of the promi- 
nences may fall into the jaws of the slit; 
and the brightness of these lines or images 
is independent of the dispersive power of the 
spectroscope, since increase of dispersion 
merely sets the images farther apart with- 
out making them fainter. The spectrum 
of the aerial illumination, on the other hand, 
is simply that of sunlight, — a continuous 
spectrum showing the usual Fraunhofer lines, and this spectrum is 
made faint by its extension. Moreover, it presents dark lines or spaces 
just at the very places in the spectrum^ where the bright images of the promi- 
nences fall, so that they become easily visible. 

A grating spectroscope of 
ordinary power, attached to 
a telescope of three or four 
inches aperture, gives a very 
satisfactory view of these 
beautiful and interesting ob- 
jects. The red image, which 
corresponds to the C line of 
hydrogen, is by far the best 
for such observations . When 
the instrument is properly 
adjusted, the slit open a little, 
and the image of the sun's 
limb brought exactly to its 
edge, the observer at the 
eye-piece of the spectroscope 
will see things about as we 
have attempted to represent them in Fig. 130, as if he were looking 
at the clouds in an evening sky from across the room through a 
slightly opened window blind. 




Fig. 130. — The Chromosphere and Prominences 
seen in the Spectroscope. 



§ 502] AREAL, LINEAR, AND ANGULAR VELOCITIES. 373 

502. Areal, Linear, and Angular Velocities (supplementary to 
Art. 249). — The number of units of area (acres or square 
miles) included in the sector of the orbit described in a unit 
of time is called the body's areal velocity. The linear velocity 
is simply the " speed ' ' with which it is moving — the number 
of feet or miles per second — and is called " linear " because 
it is measured in "linear units." The angular velocity is the 
number of angular units (degrees, or " radians ") swept over 
by the radius vector in a unit of time. 

In Fig. 131 the area of the sector ASB is the areal velocity ; 
the length of the line AB is the linear velocity ; and the angle 
ASB is the angular velocity {A 
and B are supposed to be occupied 
by the body in two successive 
seconds). 

Since the area described in a 
unit of time is the same all through 
the orbit, it can easily be proved, 
first, that the linear velocity (usu- 
ally denoted by V) is always in- FlG 131 
versely proportional to Sb, the Linear and Angular Vel0 eitie 8 . 
perpendicular drawn from S upon 

AB, produced if necessary : secondly, that the angular velocity 
(ordinarily denoted by w) at any point of the orbit is inversely 
proportional to the square of AS, the radius vector. 

In every case of motion under central force we may say, therefore : 

I. The areal velocity {acres per second) is constant. 

II. The linear velocity (miles per second) varies inversely as the dis- 
tance from the centre of force to the body's line of motion at the moment. 

III. The angular velocity (degrees per second) varies inversely as 
the square of the radius vector. 

These three statements are not independent laws, but only geomet- 
rical equivalents for each other. They hold good regardless of the 
nature of the force, requiring only that when it acts it act directly 
towards or from the centre, so as to be directed always along the line 




374 APPENDIX. [§ 502 

of the radius vector. It makes no difference whether the force varies 
with the square or the logarithm of the distance ; whether it is increas- 
ing or decreasing, attractive or repulsive, continuous or intermittent, 
provided only it be always " central." 

503. Proof of the Law of Inverse Squares, from Kepler's 
Harmonic Law (supplementary to Art. 253). — For circular orbits 
the proof is very simple. From equation (6), Art. 250, we 
have for the first of two planets, 

/. = V£ 

in which f x is the central force (measured as an acceleration), 
and i\ and t ± are respectively the planet's distance from the sun 
and its periodic time. 
For a second planet, 

H 
Dividing the first equation by the second, we get 

But by Kepler's third law 

t 2 r 3 

ti : *2 = r? : r 2 3 ; whence, -f~ 2 = \ ; 

h r i 

t 2 
substituting this value of -^ in the preceding equation, we 

have 

/i _ n v T 2 _ r i . 
f 2 r 2 7\ 3 r x 2 

i.e., fi'.f 2 = r 2 : r 2 , — which is the law of inverse squares. 

In the case of elliptical orbits the proposition is equally 
true if, for r, we substitute a, the semi-major axis of the orbit: 
but the demonstration is more complicated. 



§504] 



CORRECTION TO KEPLER S THIRD LAW. 



375 



504. Correction to Kepler's Third Law (supplementary to Art. 
253). — The Harmonic Law as it stands in Art. 251 is not 
strictly true : it would be so if the planets were mere particles, 
infinitesimal as compared with the sun; but this is not the 
case. The accurate statement is 

t{\M + m x ) : t 2 \M + m 2 ) = r* : r 2 % 

in which M is the sun's mass, and m l and m 2 are the masses of 
the two planets compared. 

505. Newton's Verification of the Idea of Gravitation by 
means of the Moon (supplementary to Art. 255). — Eegarding 
the moon's orbit as a circle, we can easily compute how much 
she falls toward the earth in 
a second. 

In Fig. 132 let AE be the 
distance the moon travels in 
a second, then DE, or its 
equal (sensibly) AB, is the 
virtual " fall " of the moon 
towards the earth in one sec- 
ond; i.e., the amount by 
which the earth's attraction 
deflects the moon away from 
the rectilinear path which it 
would otherwise pursue. By 
Geometry, since the triangle 
AEF (being inscribed in a 
semi-circle) is right-angled 
at E, we have 




Fig. 132. 

Verification of the Hypothesis of Gravitation 
by Means of the Motion of the Moon. 



AB : AE : : AE : AE or AB = 



(AE) 2 
2R 



R being the radius of the orbit. Now AE is found by divid- 
ing the circumference of the circle 2irR by T, the number of 
seconds in a sidereal month; 



376 APPENDIX. [§ 505 

whence (AE) 2 = — , and AB, which is found by dividing 

2lt*R 

this by 2R, comes out = — • If for R we put its equiva- 
lent 60 x r (r being the radius of the earth), we have, finally, 



Working out this formula with the now known values of r and 
T, we get AB = 0.0534 inches — which is quite as near to 

193 

— — - as could possibly be expected; i.e., the moon does fall 

towards the earth in a second just as much as a stone at that 
distance from the earth's centre ought to, if the hypothesis of 
gravitation is correct. 

506. The Conic Sections (supplementary to Art. 256). — (a) If 
a cone of any angle (Fig. 133) be cut by a plane which 
makes with its axis, VC, an angle greater than BVC, the semi- 
angle of the cone, the section is an ellipse (as EF). In this 
case, the plane of the section cuts completely across the cone. 
The ellipse formed will vary in shape and size according to 
the position of the plane, — the circle being simply a special 
case when the cutting plane is perpendicular to the axis. 

(b) When the cutting plane makes with the axis an angle 
less than BVC (the semi-angle of the cone), it plunges contin- 
ually deeper into the cone and never comes out on the other side, 
the cone being supposed to be indefinitely prolonged. The 
section in this case is a hyperbola, GHK. If the plane of 
the section be produced upward, however, it encounters " the 
cone produced," cutting out from it a second hyperbola, 
G'H'K', exactly like the original one, but turned in the oppo- 
site direction. The axis of the hyperbola is always reckoned 
as negative, lying outside of the curve itself (in the figure it 
is the line HH'). The centre of the hyperbola is the middle 
point of this axis, a point also outside the curve. 



506] 



ELEMENTS OF A PLANET S ORBIT. 



377 




Fig. 133. — The Conies. 



(c) When the angle made 
by the cutting plane with the 
axis is exactly equal to the 
cone's semi-angle, the plane 
will be parallel to a plane 
which is tangent to the coni- 
cal surface, and we then get 
the special case of the parab- 
ola, which is, so to speak, 
the boundary or partition be- 
tween the infinite variety of 
ellipses and hyperbolas which 
can be cut from a given cone. 
All parabolas are of the same 
shape, just as all circles are, 
differing only in size. 

This fact is by no means 
self-evident, and we cannot 
stop to prove it ; but it is true. 
It does not mean, of course, 
that an arc of a parabola has 
the same shape as an arc of 
another parabola taken from a 
different part of the curve, but 
that the complete parabolas, 
cut from infinitely extended 
cones, are similar, whatever 
the angle of the cone. 



507. Elements of a Planet's Orbit (supplementary to Art. 296). 
— In order to describe a planet's orbit intelligibly, and 
to supply the data required for the prediction of its position 
at any time, it is necessary to know certain quantities called 
the "elements" of its orbit. Those ordinarily employed are 
seven in number, as follows : — 



378 APPENDIX. [§ 507 

1. The semi-major axis ... a. 

2. The eccentricity . . . e. 

3. The inclination of the orbit to the plane of the ecliptic . . . i. 

4. The longitude of the ascending node ... &. 

5. The longitude of perihelion . . . p. 

6. The epoch . . . E. 

7. The sidereal period (or else the mean daily motion) . . . T, 
or else //,. 

The first five of these describe the orbit itself ; the two last 
furnish the means of finding the planet's place in the orbit. 
The semi-major axis determines the orbit's size; the eccen- 
tricity defines its shape; the inclination and longitude of the 
node, taken together, determine the position of the plane of the 
orbit; and, finally, the longitude of perihelion determines how 
the major axis (or line of apsides) of the orbit lies upon this 
plane. 

To determine the place of the planet in the orbit we need 
two more data. One is the starting-point or " epoch" which 
is simply the longitude of the planet at some given date 
(usually Jan. 1st, 1850). The other is commonly the time of 
revolution ; though, instead of it, we may use the mean daily 
motion. 

If Kepler's Harmonic Law were strictly true, the period 
could at once be found from the major axis by the proportion 

(1 year) 2 : T 2 : : (earth's distance from the sun)* : o 3 

(Art. 251), which gives T (in years) = a% a being expressed 
in astronomical units. But as the law is only approximate 
(Art. 504), a and T must be treated as independent quantities 
where precision is needed. 

Having these seven elements of a planet's orbit, it would be 
possible, were it not for perturbations, to compute exactly the 
precise place of the planet for any date whatever, either in 
the past or future. 



§ 507*] THE CRITICAL OR PARABOLIC VELOCITY. 379 

507*. (Supplementary to Art. 259.) The Critical or Parabolic 
Velocity, and its Relation to the Major Axis of the Orbit. — If 

we let U represent the "critical velocity" due to the attraction be- 
tween two bodies, M and m, at the distance r ; V, the velocity of m 
at that point, relative to M considered as fixed ; and a, the semi- 
major axis of the conic described by m relative to M ; then it can be 

r / U 2 \ 
proved that a = - ( — — 1 (1), — a relation of great importance. 

If V = U, the denominator becomes zero, a becomes infinite, and 
the corresponding conic is a parabola. For this reason U is generally 
called the "parabolic velocity" corresponding to the distance r. 

If V exceeds U, the denominator becomes negative, making a also 
negative, and indicating an hyperbolic orbit. 

If, however, V is less than U, the denominator will be positive and 
finite ; a will be so also, and the orbit will be an ellipse, in which m 
will revolve around M with a regular period. Moreover, since only 
r, V, and U appear in the equation which gives the value of a, it is 
clear that a, and therefore the period also according to Kepler's third 
law, are independent of everything else, — as, for instance, of the 
direction in which m is moving when its distance from M is equal to r. 

Finally, if the orbit is circular, a must equal r ; which requires that 
V 2 = \ U 2 , and V = U Vj = 0.707 x U. In other words, the velocity 
of a planet moving in a circular orbit around the sun at a distance r, 
is .707 of the " parabolic velocity " due to the sun's attraction at 
that distance. 

This " parabolic velocity " at the distance r is sometimes also called 
the " velocity from infinity" because it is that which would be ac- 
quired by a particle m in falling towards M from an infinite distance 
until it reaches a distance equal to r ; supposing, of course, that M 
is fixed and that m starts from rest and is not acted upon during 
its fall by any force except the mutual attraction between itself and 
M. It might be supposed that this " velocity from infinity " would 
itself be infinite, but it is not. Its value is given by the equation 

U=k-K— (2), in which k is a constant factor depending 

upon the units in which velocity, distance, and time are measured. 
In the solar system, if we take the mass of the sun as the unit of 
mass and the radius of the earth's orbit as the unit of distance, then 



380 APPENDIX. [§ 507 

for the velocity acquired by a particle falling freely towards the sun 
from an infinite distance to the distance r, we have 

U (miles per second) = 26.156( — J. 

If r is unity, 17= 26.156 miles per second, so that if the earth's 
velocity were increased to this, it would fly off in a parabola. At a 
distance one-fourth that of the earth from the sun, U = 52.3, and at 
the surface of the sun (where r = ^tt.t) ^ * s ^83 ; while at Neptune 
(r = 30.05), U = 4.77 miles a second. 

Formula (2) enables us also to compute the parabolic velocity at 
the surface of a planet due to its own attraction. Thus for the earth 
we put M = 3 3 T Yoo' aR d r — 2"5tto (Art. 178). U then comes out 
6.9 miles per second ; and since this is the velocity which a body 
would attain in falling under her attraction from an infinite distance 
to her surface, it follows that a body projected from the earth with 
this or any higher velocity would never return, unless brought back 
by other forces than her attraction. At the surface of the moon the 
" parabolic velocity" due to the moon's attraction is only 1.48 miles, 
or less than 8000 feet ; and this probably explains (Art. 161) why 
she has lost her atmosphere. 

508. Formula for the Mass of a Planet (supplementary to 
Art. 309). — The derivation of the formula for a planet's mass is very 
simple in the case of circular orbits. From the law of gravitation we 
have the accelerating force with which the planet and satellite attract 
each other (Art. 102) , given by the equation, 

in which P t and s x are the masses of the planet and satellite, and R x 
the radius of its orbit. Also from equation b (Art. 250), for a body 
moving in a circle, 

f WR< 

J / 2 * 

Equating these values of/, we get 

4_E% . (Pt + «,) . whe „ce (P, + ,,) = ^l. 



§ 508] FORMULA FOR THE MASS OF A PLANET. 381 

For a second planet and satellite we should get similarly 

h 
whence we have 

h h 
This is equally true of elliptical orbits, provided we put a x and a 2 for 
i?! and R 2 ; but the proof of that statement is beyond our reach here. 

509. Danger from Comets. — It has been supposed that a comet 
might damage the earth in either of two ways, — by actually striking 
us, or by falling into the sun and so causing a sudden and violent 
increase of solar radiation. 

There is no question that a comet may strike the earth, and it is 
very probable that one will do so at some time. Biela's Comet is not 
the only one whose orbit passes ours at a distance less than the comet's 
semi-diameter. Such encounters will be rare, however, — Babinet says 
once in about 15,000000 years in the long run. 

As to the consequences of a comet's striking the earth, everything, 
so far as the earth is concerned (it will certainly be bad for the comet), 
depends upon the size of the " particles " of which it is composed. If 
they weigh tons, the bombardment will be serious ; if only pounds, 
they will perhaps do some mischief. If only ounces or grains, they 
would burn in the air like shooting stars, and we should simply have 
a beautiful meteoric shower, — and this is decidedly the most probable, 
as well as the most comfortable, hypothesis. 

As regards the fall of a comet into the sun, it is practically certain 
that it will do us no harm whatever. The total amount of energy 
due to the striking of the sun by a comet having a mass to onr o o *^at 
of the earth would be only about as much as the sun radiates in eight 
or nine hours ; and the transformation of this energy into heat would 
take place almost entirely beneath, or at least within, the photosphere, 
and would appear not so much in a rise of temperature and increase 
of radiation as in an expansion of the sun f s volume. Probably if a 
comet were to strike the sun, we should know nothing of it, unless 
some observer happened to be watching the sun at the moment. He 
might see a sudden increase of brilliance on a certain portion of the 
surface, lasting for a few minutes, and very likely our magnetometers 
would show a disturbance. 



382 TWILIGHT. [§ 509* 

509*. Twilight. — This is caused by the reflection of sunlight 
from the upper portions of the earth's atmosphere. After the sun has 
set, its rays, passing over the observer's head, still continue to shine 
through the air above him, and twilight continues as long as any por- 
tion of this illuminated air remains visible from where he stands. It 
is considered to end when stars of the sixth magnitude become visible 
near the zenith, which does not occur until the sun is about 18° below 
the horizon : but this is not strictly the same for all places. 

The length of time required by the sun after setting to reach this 
depth of 18° below the horizon, varies with the season and with the 
observer's latitude. In latitude 40° it is about 90 minutes on March 
1st and Oct. 12th ; but more than two hours at the. summer solstice. 
In latitudes above 50°, when the days are longest, twilight never quite 
disappears, even at midnight. On the mountains of Peru, on the 
other hand, it is said never to last more than half an hour. 



§ 510] sun's distance. 383 



CHAPTER XVII. 

methods of determining the parallax and dis- 
tance OF the sun and stars. 

importance and difficulty of the problem. — his- 
torical. — CLASSIFICATION OF METHODS. — GEOMETRI- 
CAL METHODS. — OPPOSITIONS OF MARS AND TRANSITS 
OF VENUS. — GRAVITATIONAL METHODS. — DETERMI- 
NATION OF STELLAR PARALLAX. 

510. In some respects the problem of the sun's distance is 
the most fundamental of all that are encountered by the as- 
tronomer. It is true that many important astronomical facts 
can be ascertained before it is solved : for instance, by methods 
which have been given in Arts. 299 and 300, we can determine 
the relative distances of the planets and form a map of the solar 
system, correct in all its proportions, although the unit of meas- 
urement is still undetermined, — a map witJiout any scale of miles. 
But to give the map its use and meaning, we must ascertain 
the scale, and until we do this we can have no true conception 
of the real dimensions, masses, and distances of the heavenly 
bodies. Any error in the assumed value of the astronomical 
unit propagates itself proportionally through the whole system, 
not only solar but stellar. 

The difficulty of the problem is commensurate with its im- 
portance. It is no easy matter, confined as we are to our little 
earth, to reach out into space and stretch a tape-line to the 
sun. In Arts. 127 and 355 we have already given the two 
methods of determining the sun's distance, which depend on 



384 APPENDIX. [§ 510 

our experimental knowledge of the velocity of light. They 
are satisfactory methods and sufficient for the purposes of the 
text. But methods of this kind have become available only 
since 1849. Previously astronomers were confined entirely to 
purely astronomical methods, depending either upon geomet- 
rical measurement of the distance of one of the nearer planets 
when favorably situated, or else upon certain gravitational re- 
lations which connect the distance of the sun with some of 
the irregular motions of the moon, or with the earth's power 
of disturbing her neighboring planets, Venus and Mars. 

511. Historical. — Until nearly 1700 no even approximately 
accurate knowledge of the sun's distance had been obtained. 
Up to the time of Tycho it was assumed (on the authority of 
Ptolemy, who rested on the authority of Hipparchus, who in his 
turn depended upon an erroneous observation of Aristarchus) 
that the sun's horizontal parallax is 3', a value more than 20 
times too great. Kepler, from Tycho's observations of Mars, 
satisfied himself that the parallax certainly could not exceed 
1', and was probably much smaller; and at last, about 1670, 
Cassini, also by means of observations of Mars made in France 
and South America for the purpose, showed that the solar 
parallax could not exceed 10". He set it at 9".5, — the first 
reasonable approximation to the true value, though still about 
eight per cent too large. 

The transits of Venus in 1761 and 1769 furnished data that 
proved it to lie between 8" and 9", and the discussion of all 
the available observations, published by Encke about 1824, 
gave as a result for the parallax, 8".5776, corresponding to a 
distance of about 95,000000 miles. The accuracy of this de- 
termination was, however, by no means commensurate with the 
length of the decimal, and its error began to be obvious about 
1860 ; since then it has been practically settled that the true 
value of the sun's parallax lies somewhere between 8". 75 and 
8".85, its distance being between 92,400,000 and 93,500,000 



§ 511] PARALLAX OF THE SUN. 385 

miles. Indeed it is now certain that the figure 8 ".8, adopted 
in the text, must be extremely near the truth. 

512. The methods available for determining the distance of 
the sun may be classified under three heads, — geometrical, 
gravitational, and physical. The physical methods (by means 
of the velocity of light) have been already discussed (Arts. 
127 and 355). We proceed to present briefly the principal 
methods that belong to the two other classes. 

GEOMETRICAL METHODS. 

513. The direct geometrical method of getting the sun's 
parallax (by observing the sun itself at stations widely sepa- 
rated on the earth, in the same way that the parallax of the 
moon is measured — Art. 149) is practically worthless, the 
inevitable errors of observation being too large a fraction of 
the quantity sought. We may add that the sun, on account 
of the effect of its heat upon an instrument, is a very intracta- 
ble subject for observation. 

Since, however, we know at any time the distance of the planets 
in astronomical units, our end will be just as perfectly obtained 
by measuring the distance (in miles) of one of them. 

514. Observations of Mars. — In the case of Mars at the time 
of its nearest approach to the earth this can be done satisfac- 
torily. There are two ways of proceeding : — 

1. By observations made from two or more stations widely 
separated in latitude. 

2. By observations from a single station near the equator. 
In the first case the observations may be (a) meridian circle 

observations of the planet's zenith distance, precisely such as 
are used for getting the moon's parallax in Art. 149, just 
cited ; or they may be (b) micrometer measurements of the dif- 
ference of declination between the planet and the surrounding 
stars. 



386 



APPENDIX. 



[§514 



Since, however, different observers and different instruments 
are concerned in the observations, the results of both these 
processes seem to be less trustworthy than those obtained by 
the second method. 



\M 



515. In the second case, a single observer, by 
measuring with a heliometer (Art. 543) the ap- 
parent distance between the planet and small 
stars nearly east and west of it, can determine 
its parallax, and hence its distance, with great 
accuracy. Fig. 134 exhibits the principle in- 
volved. When the observer is at A (a point on 
or near the earth's equator), the planet M is 
just rising to him, and he sees it at a, a point in 
the sky which is east of c, the point where it 
would be seen from the centre of the earth, the 
angle CMA being its horizontal parallax. On 
the other hand, 12 hours later, when the rota- 
tion of the earth has taken the observer to B 
and the planet is setting, its parallax will dis- 
place it to the west of c, and by the same amount. 
When the planet is rising, its parallax increases 
its right ascension ; when setting, it diminishes 

'it. 

Suppose for the moment that the orbital mo- 
tions of Mars and the earth are suspended, the 
planet being at opposition and as near as pos- 
sible to us. If, then, when the planet is rising we measure 
carefully its distance M e S, Fig. 135, from a star which is west 
of it, and 12 hours later measure it again, the planet being 
now at JH/ W , the difference of the two measures will give the 
distance M e M w , which is twice the parallax of the planet. 
The earth's rotation will have performed for the observer the 
function of a long journey, by transporting him in 12 hours, 
free of expense and trouble, from one station to another 8000 
miles away. 



Fig. 134. 



§515] 



TRANSITS OF VENUS. 



387 



In practice the observations are not limited to the moment 
when the planet is exactly on the horizon, and measures are 
made not from one star alone, but from a number. Moreover, 
the orbital motions, both of the earth and the planet, during 
the interval between the observations, must be taken into 
account; but this presents no considerable difficulty. 

On the whole, this method of 
determining the astronomical 
unit is about the most accurate 
of all the geometrical methods. 
Though long ago suggested by 
Flamsteed, it was first thorough- 
ly carried out by Gill at Ascension 
Island, in 1877. His result fixed 
the solar parallax at 8".783 ± 
0".015. The size of the planet's 
disc, however, interferes some- 
what with the precision of the 
necessary measurements, and it is 
found that even more accurate re- 
sults can be obtained from some 
of the asteroids which at oppo- 
sition come nearest to us. The 
observations of Iris, Sappho, 
and Victoria, made in 1889-91, 
by Gill at the Cape of Good Hope, in concert with other observers in 
Europe and America, give 8 // .802 ± 0".005. The method cannot be 
used satisfactorily with Venus, since when nearest us she is visible 
only by day, so that the small stars near her cannot be used as 
points of reference. 

516. Transits of Venus. — Now and then, however, Venus 
passes between us and the sun and "transits" the disc, as ex- 
plained in Art. 326. Her distance from the earth is then only 
about 26,000000 miles, and her horizontal parallax is between 
three and four times as great as that of the sun. If viewed 




Fig. 135. — Micrometric Comparison of 
Mars with Neighboring Stars. 



388 



APPENDIX. 



[§516 



by two observers at different stations on the earth, she will 
therefore be seen at different points on the sun's disc, and her 
apparent displacement on the disc will be the difference between 
her own parallactic displacement (corresponding to the dif- 
ference in distance between the two stations) and that of the 
sun itself. This relative displacement is more than 2\ times 
the parallax of the sun, or, more exactly, |^f as great. 

In other words, if two observers 
are situated so far apart that the 
distance between them would sub- 
tend an angle of 8", as seen from 
the sun, then the apparent dis- 
placement of Venus on the sun's 
disc, as seen from their two sta- 
tions, would be 2.61 times 8", or 
nearly 21", a quantity quite meas- 
urable. 

To determine the solar parallax 
then, by means of a transit of Ve- 
nus, we must find the means of somehow measuring the 
angular distance between the two positions which Venus occu- 
pies on the sun's disc, as seen simultaneously from two widely 
distant stations of known latitude and longitude. The meth- 
ods earliest proposed and executed depend upon observations 
of the times of contact between the planet and the edge of the 
sun's disc. There are four of these contacts, as indicated in 
Fig. 136, the first and fourth being " external," the second and 
third "internal." 




Fig. 136. 
Contacts in a Transit of Venus. 



517. Halley's Method, or the Method of Durations. — The 

method suggested by Halley, who first noticed, in 1679, the 
peculiar advantages that would be presented by a transit of 
Venus as a means of finding the sun's distance, consists in 
observing the duration of the transit at two stations differing 
greatly in latitude, and so chosen that the difference of dura- 



§ 517] halley's method. 389 

tions will be as large as possible. It is not necessary to know 
the longitude of the stations very accurately, since absolute 
time does not come into the question. All that is necessary 
is to know the latitudes accurately (which were easily obtained 
even in Halley's time), and the clock-rates for the four or five 
hours between the beginning and end of the transit. Halley 
expected to depend mainly on the second and third contacts, 
which he supposed could be observed within a single second. 
If so, the sun's parallax could easily be determined within -^^ 
of its true value. 

Having the durations of the transit at the two stations, and know- 
ing the angular motion of Venus in an hour, we have at once very 
accurately the length of the two chords ac and df (Fig. 137) de- 
scribed by Venus upon the sun, expressed in seconds of arc — more 
accurately than they could be measured by any micrometer. We also 



S-J 




* 



B 

(Earth) 



Fig. 137. — Halley's Method. 

know the sun's semi-diameter in seconds, and hence in the triangles 
Sab and Sde, we can compute the length (in seconds still) of Sb and 
Se. Their difference, be, is the displacement due to the distance 
between the stations on the earth. The virtual base line is of 
course not the direct distance between B and E, because that line is 
not perpendicular to the line of sight from the earth to Venus, but 
the true value to be used is easily found by Trigonometry. Calling 
this true base line m, and putting p" for the sun's horizontal parallax, 
we have 

J>"=P«]"x.(fg)x 

r being the radius of the earth. The rotation of the earth of course 
comes in to shift the places of E and B during the transit, but the 
shift is easily allowed for. 



390 



APPENDIX. 



[§51? 



In order that the method may be practically successful, it is also 
necessary that the transit tracks should lie near the edge of the sun. 
for obvious reasons. If they crossed near the centre of the disc, it 
would be impossible to compute the distances, Sb and Se, with much 
accuracy. 

Halley died before 
the transits of 1761- 
69, but his method 
was thoroughly tried, 
and it was found that 
the observations of 
contact, instead of be- 
ing liable to an error 
of a single second, are 
uncertain to fully 10 
times that amount. 
This is due to the 
fact that at the time 
of internal contact the 
planet does not pre- 
sent the appearance 
of a round, black disc 
neatly touching the 
edge of the sun, but 
is slightly distorted by optical imperfections of the telescope 
and of the observer's eye ; and, moreover, it is surrounded by 
an undefined, luminous ring, caused by the refraction of sun- 
light through its atmosphere, — a very beautiful phenomenon, 
but quite incompatible with accurate observation of "con- 
tacts." Fig. 138 illustrates the appearances seen by Vogel 
during the transit of 1882. 

518. De l'lsle's Method. — Halley's method requires stations 
in high latitudes, uncomfortable arid hard to reach, and so 
chosen that both the beginning and end shall be visible. More- 





Fig. 138. 



-Atmosphere of Venus as seen during a 
Transit. (Vogel, 1882.) 



§ 518] HELIOMETRIC OBSERVATIONS. 391 

over, if the weather prevents the end from being visible after 
the beginning has been observed, the method fails. 

De l'Isle's method, on the other hand, employs pairs of 
stations near the equator, and does not require that the ob- 
server should see both the beginning and end of the transit. 
Observations of either phase can be utilized, which is a great 
advantage. But it does require that the longitudes of the 
stations should be known with extreme precision, since it con- 
sists essentially in observing the absolute time of contact (i.e., 
Greenwich or Paris time) at both stations. 

Suppose that an equatorial observer, E, Fig. 139, on one 
side of the earth notes the moment of internal contact in 
Greenwich time, the planet being then at Vi ; when W notes 
the contact (also in Greenwich time), the planet will be at 
V 2 , and the angle ViDV 2 is the earth's apparent diameter as 
seen from the sun; i.e., twice the sun's horizontal parallax. Now 




Fig. 139. — De l'Isle's Method. 

the angle at D is at once determined by the time occupied by 
Venus in moving from V L to V 2 - It is simply just the same 
fraction of 360°, that the lime is of 584 days, the planet's syn- 
odic period. If, for example, the time were 12 minutes, we 
should find the angle at D to be about 18". 

519. Heliometric and Photographic Observations. — Instead 
of observing merely the four contacts and leaving the rest of 
the transit unutilized, we may either keep up a continued 
series of measurements of the planet's position upon the sun's 
disc with a heliometer, or we may take a series of photo- 
graphs to be measured up at leisure. Such heliometer meas- 



392 APPENDIX. [§ 519 

ures or photographs, taken in connection with the recorded 
Greenwich times at which they were made, furnish the means 
of determining just where the planet appeared to be on the 
sun's disc at any given moment, as seen from the observer's 
station. A comparison of these positions with those simulta- 
neously occupied by the planet, as seen from another station, 
gives at once the means of deducing the parallax. 

In 1874-82 several hundred heliometer measures were made, 
mostly by German parties, and several thousands of photo- 
graphs were obtained at stations in all quarters of the earth 
where the transits could be seen. The final result of all these 
observations l is given by Newcomb as 8".857 ±0.23, differing 
to an unexpected degree from the figures given by other 
methods, and rather discordant among themselves. It would 
almost seem that measurements of this sort must be vitiated 
by some constant source of error. 

520. Gravitational Methods. — These hardly admit of ele- 
mentary discussion. We merely mention them. 

1. By the moon's parallactic inequality. This is an irregu- 
larity in the moon's motion, which depends simply on the ratio 
between the distance of the sun and the radius of the moon's 
orbit. If, what is practically very difficult, we could determine 
by observation exactly the amount of this inequality (which 
reaches about 2 f at its maximum), we could at once get the 
solar parallax. 

2. The perturbations produced by the earth in the motions 
of Mars and Venus give the means of determining the ratio 
between the mass of the sun and that of the earth. Now 
from Art. 309, 



S:E-. 



T 2 ' t 2 ' 



1 The more than 2000 photographs which were made during the two 
transits at the stations occupied by American parties give a solar parallax 
of 8". 84. 



§ 520] MEASURING STELLAR PARALLAX. 393 

in which S and E are respectively the masses of the sun and 
earth, R and r are the radii of the orbits of the earth and 
moon, T is* the length of the sidereal year, and t that of the 
sidereal month, corrected for perturbations. Hence 

- (or M ) = *- X — • 

If, then, Jf is known from planet observations, R is at once 
deducible in terms of r (moon's distance). 

There are also other equations available which do not in- 
volve the moon at all, but substitute measurements of gravity 
by the pendulum. 

Even at present this method approaches closely in value to 
the others. Ultimately, it must supersede them all, because 
as time goes on and the secular perturbations of our two 
neighboring planets accumulate, the precision with which M 
is determined continually improves, and apparently without 
limit. 



METHODS OF MEASURING STELLAR PARALLAX. 

521 (supplementary to Art. 432) . The determination of stellar 
parallax had been attempted over and over again from the 
time of Tycho Brahe down, but without success, until in 1838 
Bessel at last demonstrated and measured the parallax of 61 
Cygni ; and the next year Henderson of the Cape of Good 
Hope, determined that of Alpha Centauri. The operation of 
measuring the parallax of a star is on the whole the most 
delicate in the whole range of practical astronomy. Two 
methods have been successfully employed so far, known as the 
absolute and the differential. 

(a) The first method consists in making meridian observations of 
the star's right ascension and declination with the extremest possible 
accuracy, at different times of the year, applying rigidly all the known 



394 APPENDIX. [§ 621 

corrections (for precession, nutation, proper motion, etc.) and then 
examining the deduced positions. If the star is without parallax, 
they will all agree. If it has sensible parallax, they will show, when 
plotted on a chart, an apparent annual orbital motion of the star and 
will determine the size of its "parallactic orbit" (Art. 432). Theo- 
retically this method is perfect : practically it seldom gives satisfactory 
results, because the annual changes of temperature and moisture dis- 
turb the instrument in such a way that its errors intertwine themselves 
with the parallactic displacement of the star in a manner that defies 
disentanglement. No process of multiplying observations and taking 
averages helps the matter very much, because the instrumental errors 
involved are themselves annually periodic, just as is the parallax itself. 
Still, in a few cases, the method has proved successful, as in the case 
of Alpha Centauri, above cited. 

522. (b) The Differential Method. — This consists in meas- 
uring the change of position of the star whose parallax we are 
seeking, with respect to other small stars, near it in apparent 
position (i.e., within a few minutes of arc), but presumably so 
far beyond as to have no sensible parallax of their own. The 
great advantage of the method is that it avoids entirely the 
difficulties due to the uncertainty in respect to the precise 
amount of the corrections for precession, aberration, nutation, 
etc., since these are sensibly the same for the principal star 
as for the comparison stars ; to a considerable extent also, the 
method evades the effects of refraction and temperature dis- 
turbances. But per contra, it measures not the whole parallax 
of the star investigated, but only the difference between its par- 
allax and that of the stars with ivhich it is compared. 

Suppose, for instance (see Fig. 140), that in the same telescopic 
field of view, we have the star a, which is near us, the stars c, d, and e, 
which are so remote that they have no sensible parallax at all, and the 
star b, which is about twice as far away as a. a and b will describe 
their parallactic orbits every year, just alike in form, but a's orbit 
twice as large as 6's. If now, during the year, we continually measure 
the distance (in seconds of arc) and the direction from c or e to a and 
6, the results will give us the true dimensions of their parallactic 



§ 522] STELLAR PARALLAX. 395 

orbits. If, however, we had taken b as the starting point to measure 
a's motion, we should have found only half the true value. It follows 
that if the measurements are absolutely accurate, the parallax deduced 
by this method can never be too large, but may be too small : the dis- 
tance of the star will certainly be more or less exaggerated. 





l^zzt— 




i' 


Mr 


___- — 7*r ~/ ' 







0* 


\ \ 




2 (b) 




\ 


\ 






\ 
\ 


\ 






\ 


\ 






\ 


\ 






\ 


\ 

V \ 
\\ 

e 





Fig. 140. — Differential Method of determining Stellar Parallax. 

The necessary measurements, if the comparison stars are 
within a minute or two of arc from the star under investiga- 
tion, may be made with, the wire micrometer ; but if the 
distance exceeds a few minutes, we must resort to the " helio- 
meter" (Appendix, Art. 543) with which Bessel first suc- 
ceeded; or we may employ photography, which Professor 
Pritchard at Oxford has recently been doing with remarkable 
success. On the whole, the differential method, notwithstand- 
ing the fundamental objection to it which has been mentioned, 
is much more trustworthy than the other. 

523. Selection of Stars to be examined for Parallax. — It is 

obviously necessary to choose for observations of this sort stars that 
are presumably near. The most important indication of proximity is 
a large proper motion. Brightness also is of course confirmatory. Still, 
neither of these indications is certain. A star which happens to be 
moving directly towards or from us shows no proper motion at all, 
however near ; and among the millions of faint stars it is quite likely 
that some few individuals, at least, are nearer than Alpha Centauri. 



)ft6 APPENDIX. [§ 524 



CHAPTER XVIII. 

ASTRONOMICAL INSTRUMENTS. 

THE CELESTIAL GLOBE. — THE TELESCOPE: SIMPLE, ACHRO- 
MATIC, AND REFLECTING. — THE EQUATORIAL. — THE 
FILAR MICROMETER. — THE HELIOMETER. — THE TRAN- 
SIT INSTRUMENT. — THE CLOCK. — THE CHRONOGRAPH. 
— THE MERIDIAN CIRCLE. — THE SEXTANT. — THE PYR- 
HELIOMETER. 

524. The Celestial Globe. — The celestial globe is a ball, 
usually of papier-m&che, upon which are drawn the circles of 
the celestial sphere and a map of the stars. It is mounted in 
a framework which represents the horizon and the meridian, 
in the manner shown by Fig. 141. 

The "Horizon" HH' in the figure, is usually a wooden ring 
three or four inches wide and perhaps three-quarters of an inch 
thick, directly supported by the pedestal. It carries upon its 
upper surface at the inner edge a circle marked with degrees for 
measuring the azimuth of any heavenly body, the graduation 
beginning at the south point where the horizon is intersected 
by the metal circle which represents the meridian. Next 
comes the zodiacal circle, containing in order the names of the 
12 signs of the zodiac. Outside of this is a narrow circle 
marked with the degrees of celestial longitude, the zero of this 
graduation being made to correspond with the sign Aries in 
the zodiacal circle. Just outside of this circle is a second sim- 
ilar one, marked with the months of the year and the days of 
the month, the days being set against the longitude gradua- 



§ 524] 



THE CELESTIAL GLOBE. 



397 



tion so that each day is opposite to the degree of longitude 
occupied by the sun on that day of the year. In the circle of 
the months is also given at different points the equation of 
time for corresponding days. 

525. The Meridian Ring, MM 1 , is a circular ring of metal 
which carries the bearings of the axis on which the globe 
revolves. Things are so arranged, or ought to be, that the 
mathematical axis of the globe is exactly in the same plane as 




Fig. 141. — The Celestial Olobe. 



the graduated face of the ring, which is divided into degrees 
and fractions of a degree. The meridian ring fits into two 
notches in the horizon-circle, and is held underneath the globe 



398 . APPENDIX. [§525 

by a support with a clamp, which enables us to fix it securely 
in any desired position, the mathematical centre of the globe 
being precisely in the planes both of the meridian ring and 
the horizon. 

526. The Surface of the Globe is marked first with the celes- 
tial equator (Art. 27), next with the ecliptic (Art. 38), cross- 
ing the equator at an angle of 23^-° (at V in the figure), and 
each of these circles is divided into degrees and fractions. 
The equinoctial and solstitial Coheres (Art. 113), are also 
always represented. As to the other circles, usage differs. 
The ordinary way at present is to mark the globe with 24 
hour-circles, 15 degrees apart (the Colures being two of them), 
and with parallels of declination 10 degrees apart. 

On the surface of the globe are plotted the positions of the 
stars and the outlines of the constellations. 

527. The Hour Index is a small metal circle three or four 
inches in diameter, which is fitted to the northern pole of 
the globe with stifrish friction, so that it can be set like the 
hands of a clock, but once set will turn with the globe without 
shifting its adjustment. 

528. To Rectify a Globe, — that is, to set it so as to show 
the aspect of the heavens at any given time : — 

(1) Elevate the North Pole of the globe to an angle equal 
to the observer's latitude by means of the graduation on the 
meridian ring, and clamp the ring securely. 

(2) Look up the day of the month on the " horizon " of the 
globe, and opposite to the day find, on the longitude circle, the 
sun's longitude for that day. 

(3) On the ecliptic (on the surface of the globe) find the 
degree of longitude thus indicated and bring it to the gradu- 
ated face of the meridian ring. 

The globe is then set to correspond to (apparent) noon of 



§ 528] THE TELESCOPE. 399 

the day in question. (It may be well to mark the place of the 
sun temporarily with a bit torn from the corner of a postage- 
stamp, and gummed on at the proper place in the ecliptic : it 
can easily be wiped off with a damp cloth, after using.) 

(4) Holding the globe fast, so as to keep the place of the 
sun on the meridian, turn the hour index until it shows at the 
edge of the meridian ring the mean time of apparent noon; 
i.e., 12 h ± the equation of time given for the day on the hori- 
zon ring. If standard time is used, the hour index must be 
set to the standard time of apparent noon. 

(5) Finally, turn the globe until the hour for which it is 
to be set is brought to the meridian, as indicated on the hour 
index. The globe will then show the true aspect of the 
heavens. 

The positions of the moon and planets are not given by this 
operation, since they have no fixed places in the sky and there- 
fore cannot be put in by the globe-maker. If one wants them 
represented, he must look up their right ascensions and decli- 
nations for the day in some almanac, and mark the correspond- 
ing places on the globe with bits of wax or paper. 

TELESCOPES. 

529. Telescopes are of two kinds, refracting and reflecting. 

The refractor was first invented, early in the 17th century, 
and is much more used ; but the largest instruments ever made 
are reflectors. In both, the fundamental principle is the same. 
The large lens of the instrument (or else its concave mirror) 
forms a real image of the object looked at, and this image is 
then examined and magnified by the eye-piece, which in prin- 
ciple is only a magnifying glass. 

In the form of instrument, however, which was originally devised 
by Galileo and is still used as the " opera-glass," the rays from the 
object-glass are intercepted, and brought to parallelism by the concave 
lens, which serves as an eye-glass, before they form the image. Tele- 



400 APPENDIX. [§ 529 

scopes of this construction are never made of any considerable power, 
being very inconvenient on account of the smallness of the field of 
view. 

530. The Simple Refracting Telescope. — This consists es- 
sentially, as shown in Fig. 142, of two convex lenses ; one, the 
object-glass A, of large size and long focus ; the other, the 
eye-glass B, of short focus, — the two being set at a distance 
nearly equal to the sum of their focal lengths. Kecalling the 
optical principles relating to the formation of images by lenses 
(Physics, p. 360), we see that if the instrument is pointed 
towards the moon, for instance, all the rays that strike the 
object-glass from the top of the crescent will be collected to a 
focus at a, while those from the bottom will come to a focus at 
b ; and similarly with rays from the other points on the surface 




nr 

Fig. 142. — The Simple Refracting Telescope. 

of the moon. We shall, therefore, get in the " focal plane " of 
the object-glass a small inverted "image" of the moon. The 
image is a real one; i.e., the rays really meet at the focal points, 
so that if we insert a photographic plate in the focal plane at 
ab and properly expose it, we shall get a picture of the object. 
The size of the picture will depend upon the apparent angular 
diameter of the object and the distance from the object-glass 
to the image ab, and is determined by the condition that, as 
seen from the point (the "optical centre" of the object-glass), 
the object and its image subtend equal angles, since rays which 
pass through the point suffer no sensible deviation. 

If the focal length of the lens A is 10 feet, then the image of the 
moon formed by it w T ill appear, when viewed from a distance of 10 
feet, just as large as the moon itself : viewed from a distance of one 



§ 530] MAGNIFYING POWEB. 401 

foot, the image will, of course, appear 10 times as large. With such an 
object-glass, therefore, even without an eye-piece, one can see the 
mountains of the moon and the satellites of Jupiter by simply putting 
the eye in the line of the rays, at a distance of 10 or 12 inches back of 
the eye-piece hole (the eye-piece having been, of course, removed). 

531. Magnifying Power. — If we use the naked eye, Ave 
cannot see the image distinctly from a distance much less 
than a foot, but if we use a magnifying lens of, say, one inch 
focus, we can view it from a distance of only an inch, and it 
will look correspondingly larger. Without stopping to prove 
the principle, we may say that the magnifying power is sim- 
ply equal to the quotient obtained by dividing the focal length of 
the object-glass by that of the eye-lens ; or, as a formula 

M = - ; that is, — in the figure, 
/ cd 

If, for example, the focal length of the object-glass be four 
feet and that of the eye-lens one-quarter of an inch, then 

Jf=^=192. 

i 

4 

It is to be noted, however, that a magnifying power of unity is 
sometimes spoken of as no magnifying power at all, since the image 
appears of the same size as the object. 

The magnifying power of a telescope is changed at pleasure by 
simply interchanging the eye-pieces, of which every telescope of any 
pretensions always has a considerable stock, giving various powers. 

532. Brightness of the Image. — This depends not upon the 
focal length of the object-glass, but upon its diameter ; or, 
more strictly, its area. If we estimate the diameter of the 
pupil of the eye at one-fifth, of an inch, as it is usually reck- 
oned, then (neglecting the loss from want of perfect transpar- 
ency in the lenses) a telescope one inch in diameter collects 
into the image of a star 25 times as much light as the naked 



10:2 APPENDIX, [§532 

eye receives j and the great lack telescope of ;>0 inches in 
diameter, 32,400 times as much, or about 25,000 after allow- 
ing for the Losses. The amount of light is proportional to the 
square of the diameter of the object-glass. 

The apparent brightness of an object which, like the moon or 
a planet, shows a disc, is not, however, increased in any such 
ratio, because the light gathered by the objeot-glass is spread 
out by the magnifying power of the eye-piece. In fact, it. can 
be demonstrated that, no optical arrangement can show an eav 
tended surface brighter than it appears to the naked eye. But 
the total quantity of Light in the image of the object greatly 
exceeds that which is available for vision with the naked eye, 
and objects which, like the stars, are mere luminous points, 

have their brightness immensely increased, so that with the 

telescope millions otherwise invisible are brought, to light. 
With the telescope, also, the brighter stars are easily seen in 

the daytime. 

533. The Achromatic Telescope. — A single lens cannot 
bring the vavs which emanate from a single point in the object 

to any exact focus, since the rays o( different, color (wave- 
length) are differently refracted, the blue more than the green, 
and this more than the red (Physics, p. 364). In consequence 
oi' this so-called "chromatic aberration," the simple refracting 
telescope is a very poor 1 instrument. 

About L760, it was discovered in England that by making 
the object-glass o( two or more lenses o\' different kinds of 
glass, the chromatic aberration can be nearly corrected. Ob- 
ject-glasses so made — none others are now in common use — 
are called achromatic, and they fulfil with reasonable approxi 

1 Hv making it extremely Long in proportion to its diameter, the indis- 
tinctness of the imago is considerably diminished, and in the middle of tlio 

17th oentUiy instruments more than 200 foot in length were used by Cas- 
siui and others. Saturn's rings and several of his satellites were discov- 
ered by lluvghens and Cassini with instruments of this kind. 



I 588] 



THE ACHROMATIC OBJECT-GLASS. 



403 





Littrow 
brown 

Clark 

Fig. 143. — Different ForrriH of the Achromatic 
Object-g]aM« 



mation the "condition of distinctness"; viz., that the rayn 
which emanate from, any single point in the object, should be col* 
lected to an absolute mathematical point in the image. In prac- 
tice, only two lenses are 
Ordinarily used in the con- 
struction of an astronomi- 
cal glass, — a convex of 
<to ten glass, and a concave 
of flint glass, the curves of 
the two lenses and the dis- 
tances between them being so chosen as to give the, most per- 
fect possible correction of the w spherical " aberration (Phys- 
ics, p. 363) as well as of the chromatic. Many forms of object- 
glass are made: three of them are shown in Pig. 14.'>. 

534. Secondary Spectrum. — It is not possible with the 
kinds of glass hitherto available to obtain a perfect correction 
of color. Even the best achromatic telescopes show a purple 
halo around the image of a bright star, which, though usually 
regarded as "very beautiful." by tyros, seriously injures the 
definition: it is especially obnoxious in large instruments. 

This imperfection of achromatism makes it impossible to get satis- 
factory photographs with an ordinary object-glass, corrected for vision. 
An instrument for photography must have an object-glass specially 
corrected for the purpose, since the rays which are most efficient in 
making the image upon the photographic plate are the blue and violet 
rays, which in the ordinary object-glass are left to wander very wildly. 

Much is hoped from the new kinds of glass now being made for 
optical purposes at Jena, Germany, as the result of the experiments 
conducted by Professor Abbe at the expense of the German govern- 
ment. Cooke & Son, English opticians, since L894 advertise "Photo- 
visual lenses which an; practically * aplanatic,' " and offer to make 
them as Large as twenty inches in diameter. Several of six or eight 

inches aperture, already constructed, have been reported On very fav- 
orably by eminent astronomers ; and larger ones are being made. 
Possibly a new era of telescope-making will open with the coming 
century. 



404 APPENDIX. [§ a34* 

534*. Diffraction and Spurious Discs. — Even if a lens were 
absolutely perfect as regards the correction of aberrations, 
both, spherical and achromatic, it would still be unable to fulfil 
strictly "the condition of distinctness." Since light consists 
of waves of finite length, the image of a luminous point can 
never be also a point, but must of mathematical necessity ac- 
cording to the laws of diffraction be a disc of finite diameter 
surrounded by a series of interference rings ; and the image of 
a line will be a streak and not a mathematical line. The diam- 
eter of the " spurious disc " of a star, as it is called, varies in- 
versely with the diameter of the object-glass, and the larger 
the telescope the smaller the image of a star with a given 
magnifying power. 

With a good telescope and a power of about 30 to the inch of aper- 
ture (120 for a 4-inch telescope) the image of a small star, when the 
air is steady (a condition unfortunately seldom fulfilled), should be a 
clean, round disc with a bright ring around it, separated from the disc 
by a clear black space. According to DaAves, the image of a star 
with a 4J-inch telescope should be about l /; in diameter; with a 9-inch 
instrument 0".5, and l" for a 36-inch glass. 

If too deep an eye-piece be used, raising the power of the telescope 
too high (more than about 60 to the inch), the spurious disc of the star 
will become hazy at the edge, so that there is very little use with most 
objects in pushing the magnifying power any higher. 

This effect of diffraction has much to do with the superiority of 
large instruments in showing minute details ; no increase of magnify- 
ing power on a small telescope can exhibit the object as sharply as the 
same power on a large one, provided, of course, that the object-glasses 
are equally good in workmanship and that the atmospheric conditions 
are satisfactory. (But a given amount of atmospheric disturbance 
injures the performance of a large telescope much more than that of 
a small one.) 

535. Eye-pieces. — For some purposes the simple convex 
lens is the best " eye-piece " possible ; but it performs well 
only for a small object, like a close double star, exactly in the 



H35] 



KVE-PIECBS. 



405 



centre of the field of view. As soon as the object is a little 
away from the centre, the image becomes hideous. Generally, 
therefore, we employ " eye-pieces " composed of two or more 
lenses, which give a larger field of view than a single lens and 
define satisfactorily over the whole extent of the field. They 
fall into two general classes, the positive and the negative. 

The positive eye-pieces are much more generally useful. 
They act as simple magnifying glasses, and can be taken out 
of the telescope and used as hand-magnifiers if desired. The 
image of the object formed by the object-glass lies outside of 
this kind of eye-piece, between it and the object-glass. 

In the negative eye-piece, on the other hand, the rays from 
the object-glass are intercepted by the so-called " field lens " 
before reaching the focus, and the image is formed between 

Steinheil 'JHonocentric* 

{Positive) 



Ramsden 

{Positive) 



T: ^m^ ir 



Fig. 144. 





- Various Forms of Telescope Eye-piece. 



the two lenses of the eye-piece. It cannot therefore be used 
as a hand-magnifier. 

Fig. 144 shows the two most ordinary forms of eye-piece, 
and also the " solid eye-piece " constructed by Steinheil ; but 
there are a multitude of other kinds. 

The ordinary eye-pieces show the object in an inverted 
position, which is of no importance as regards astronomical 
observations. 



The erecting eye-piece used in spy-glasses is constructed differently, 
having in it four lenses. It is essentially a compound microscope, 
and produces erect vision by inverting a second time the already 
inverted image formed by the object-glass. 



406 APPENDIX. [§ 535 

It is evident that in an achromatic telescope, the object-glass is by 
far the most important and expensive member of the instrument. It 
costs, according to size, from $100 or $200 up to $50,000, while the 
eye-pieces cost from $5 to $25 apiece. 

536. Reticle. — When the telescope is used for pointing 
upon an object, as it is in most astronomical instruments, it 
must be provided with a "reticle" of some sort. The simplest 
form is a metallic frame with spider lines stretched across it, 
the intersection of the spider lines being the point of reference. 
This reticle is placed not at or near the object-glass, as is often 
supposed, but in its focal plane, as a b in Fig. 142. Of course, 
positive eye-pieces only l can be used in connection with such a 
reticle. Sometimes a glass plate with fine lines ruled upon it 
is used instead of spider lines. Some provision must be made 
for illuminating the lines, or "w r ires," as they are usually 
called, by reflecting into the instrument a faint light from a 
lamp suitably placed. 

537. The Reflecting Telescope. — About 1670, when the 
chromatic aberration of refractors first came to be understood 
(in consequence of Newton's discovery of the " decomposition of 
light"), the reflecting telescope was invented. For nearly 150 
years it held its place as the chief instrument for star-gazing, 
until about 1820, when large achromatics began to be made. 
There are several varieties of reflecting telescope. They differ 
in the way in which the image formed by the mirror is brought 
within reach of the magnifying eye-piece. Fig. 145 illustrates 
three of the most common forms. The Herschelian form is 
practicable only with very large instruments, since the head 
of the observer cuts off part of the light. The Newtonian is 
the one most used, but one or two large reflectors now in use 
are of the Cassegrainian form, which is exactly like the Grego- 

1 In sextant telescopes a negative eye-piece is sometimes used, with the 
wires between the two lenses. 



§537] 



LARGE TELESCOPES. 



407 



rian shown in the figure, with the exception that the small 
mirror is convex instead of concave. 

Until about 1870, the large mirror (technically " speculum v ) 
was always made of speculum metal, a composition of copper 
and tin. It is now usually made of glass, silvered on the front 
by a chemical process. When new, these silvered films reflect 
much more light than the old speculum metal : they tarnish 
rather easily, but fortunately they can be easily renewed. 



-B 



—~^J> 



a(j, 



40 



~B 



q a > 



W 



u 






~B 



Fig. 145. — Different Forms of Reflecting Telescope. 
1. The Herschelian ; 2. The Newtonian; 3. The Gregorian. 

538. Large Telescopes. — The largest telescopes ever made have 
been reflectors. At the head stands the enormous instrument of Lord 
Rosse of Birr Castle, Ireland, six feet in diameter and 60 feet long, 
made in 1842, and still used. Next in size, but probably superior in 
power, comes the five-foot silver-on-glass reflector of Mr. Common, at 
Ealing, England, completed in 1889 ; and then follow a number (four 
or five) of four-foot telescopes, — that of Herschel (erected in 1789, but 
long ago dismantled) being the first, while the great instrument at 
Melbourne (Fig. 146) is the only instrument of this size now in active 
use. 

Of the refractors, the largest is that of the Yerkes Observatory, of 
the Chicago University. It has an aperture of 40 inches and a focal 



408 



APPENDIX. 



[§538 



length of 65 feet. Next follows that of the Lick Observatory (see 
Frontispiece) which has a diameter of 30 inches and a length of 57 
feet. The next in size is the 32-inch (visual) telescope at Meudon, 
which is followed by the Pulkowa telescope, 30 inches in diameter ; 
and this is nearly equalled by the great telescopes at Nice and Paris 
with an aperture of 29 J inches. Then come the new Greenwich tele- 




Fig. 146. — The Melbourne Reflector. 



scope, 28 inches ; the Vienna telescope, 27 inches ; the two telescopes 
at Washington and the University of Virginia, 26| inches ; and the 
Nevvall telescope (lately presented to the University of Cambridge, 
England), 25 inches. These are at present all the refractors which 
have an aperture exceeding two feet, but a number of others are now 



§ 538] REFLECTORS VS. REFRACTORS. 409 

under construction. The two largest of these object-glasses, and 
those of the Pulkowa, Washington, and University of Virginia tele- 
scopes, were made by the Clarks, as w T ell as the 24-inch telescope of 
the Lowell Observatory and the 23-inch instrument at Princeton. 

539. Relative Advantages of Reflectors and Refractors. — 

There is much earnest discussion on this point, each form of 
instrument having its earnest partisans. In favor of the reflec- 
tors we may mention 

1. Ease of construction and cheapness: the speculum lias but 
one surface to be worked, while the object-glass has four of 
them. Moreover the material of the speculum is much more 
easily obtained, since the light does not go through it as in the 
case of a lens ; so that slight imperfections of internal struc- 
ture and homogeneity are not very important. 

2. Reflectors can be made larger than refractors. 

3. Reflectors are perfectly achromatic: this is an immense 
advantage, especially in photographic and spectroscopic work. 

On the whole, however, the balance of advantage is now 
generally considered to lie with the refractors. 

1. The refractor gives a brighter image than a reflector of 
the same size. A heavy percentage of the light is lost by the 
two reflections, while in a refractor much less is lost in pass- 
ing through the lenses. 

2. Refractors generally define much better. Any error of 
form at a point in the surface of a lens, whether it be due to 
distortion by the weight of the lens or to the fault of the 
workmanship, affects the rays passing through that point only 
one-third as much as in the case of a speculum. Moreover, 
when a lens is slightly distorted by its weight, its tw r o oppo- 
site surfaces are affected in a nearly compensatory manner. 
In a mirror there is no such compensation ; the slightest dis- 
tortion of a speculum is fatal to its performance. 

3. A lens once made and fairly taken care of does not dete- 
riorate with age. A speculum, on the other hand, must be 
re-silvered or re-polished every few years. 



410 



APPENDIX. 



[§539 



4. As a rule, refractors are much more convenient to use 
than reflectors, being lighter and less clumsy. 

540. Mounting of a Telescope, — the Equatorial. — A tele- 
scope, however excellent optically, is not good for much unless 

firmly and conveniently mounted. 1 

At present some form of equatorial 
mounting is practically universal. 
Fig. 147 represents schematically 
the ordinary arrangement of the 
instrument. Its essential feature 
is that its " principal axis" (i.e., 
the one which turns in fixed bear- 
ings attached to the pier and is 
called the polar axis) is placed par- 
allel to the earth's axis, pointing to 
the celestial pole, so that the circle 
H, attached to it, is parallel to the 
celestial equator. This circle is 
sometimes called the hour-circle, 
sometimes the right-ascension circle. 
At the extremity of the polar axis 
a " sleeve " is fastened, which carries the declination axis D, 
and to this declination axis is attached the telescope tube 
T, and also the declination circle C. 

541. The advantages of this mounting are very great. In 
the first place, when the telescope is once pointed upon an 
object it is not necessary to move the declination axis at all 
in order to keep the object in the field, but only to turn the 




Fig. 147. 



The Equatorial (Schematic). 



1 We may add that it must, of course, be mounted where it can be 
pointed directly at the stars, without any intervening window-glass be- 
tween it and the object. We have known purchasers of telescopes to 
complain bitterly because they could not see Saturn well through a closed 
window- 



§541] THE EQUATORIAL. 411 

polar axis with a perfectly uniform motion, which can be, and 
usually is, given by clock-work (not shown in the figure). 

In the next place, it is very easy to find an object even if 
invisible to the eye (like a faint comet, or a star in the day- 
time), provided we know its right ascension and declination, 
and have the sidereal time, — a sidereal clock or chronometer 
being an indispensable accessory of the equatorial. We simply 
set the declination circle to the declination of the object, and 
then turn the polar axis until the hour-circle shows the proper 
hour-angle, which hour-angle is simply the difference between 
the right ascension of the object and the sidereal time at the 
moment. When the telescope has been so set, the object will 
be found in the field of view, provided a low-power eye-piece is 
used. On account of refraction, the setting does not direct 
the instrument precisely to the apparent place of the object, 
but only very near it : near enough for easy finding, however. 

The equatorial does not give very accurate positions of heav- 
enly bodies by means of the direct readings of its circles, but 
it can be used, as explained in Art. 71, to determine very pre- 
cisely the difference between the position of a known star and 
that of a comet or planet, and this answers the purpose as 
well as a direct determination. 

The frontispiece shows the actual mounting of the Lick telescope. 
Fig. 105, Art. 425, represents another form of equatorial mounting, 
adopted for several of the instruments of the photographic cam- 
paign, and Fig. 146 is a view of the great Melbourne reflector. Lord 
Rosse's six-foot telescope is not equatorially mounted. 

542. Micrometer. — Micrometers of various forms are em- 
ployed in connection with the equatorial, the most common and 
generally useful micrometer being that known as the filar-posi- 
tion micrometer (shown in Fig. 148) — a small instrument 
which screws into the eye end of the telescope. It usually 
contains a set of fixed wires, two or three of them parallel to 
each other (only one, e, is shown in Fig. 149, which represents 



412 



APPENDIX. 



[§542 



the internal construction of the instrument), crossed at right 
angles by a single line or set of lines. Over the plate which 
carries the fixed threads lies a fork, moved by a carefully made 

screw with a graduated 
head, and this fork carries 
one or more wires parallel 
to the first set, so that the 
distance between the wires 
e and d, Fig. 149, can be 
adjusted at pleasure and 
" read off " by means of 
the scale that is shown 
and the screw-head grad- 
uation. The box, B, Fig. 
148, containing the wires 
and micrometer, is so ar- 
ranged that it can itself 
be rotated around the op- 
tical axis of the telescope 
and set in any desired 
" position/' — for example, so that the movable wire d shall 
be parallel to the celestial equator. When so set that the 




Fig. 148. — The Filar Position-Micrometer. 




Fig. 149. — Construction of the Micrometer. 



movable wire points from one star to another in the field of 
view, the " position angle " is then read off on the circle, A. 

With such a micrometer we can measure at once the distance 
in seconds of arc between any two stars which are near enough 



.542] 



THE HELIOMETER. 



413 



to be seen in the same field of view, and can determine the posi- 
tion angle of the line joining them. The available range in a 
small telescope may reach 30'. In large ones, which with the 
same eye-pieces give much higher magnifying powers, the 
range is correspondingly less — from 5' to 10'. When the dis- 
tance between the objects exceeds 1' or 2', however, the filar- 
micrometer becomes difficult to use and inaccurate, and we 
have to resort to instruments of a different kind. 



543. The Heliometer. — This instrument, as its name im- 
plies, was originally designed to measure the apparent diameter 
of the sun, and is capable of measuring with extreme precision 
angular distances ranging all the way from a few seconds up 
to two or three degrees. It is a form of "double-image" 
micrometer, the measurement of the 
distance between two objects being 
made by superposing the image of one 
of them upon that of the other. In using 
the filar-micrometer we have to look 
" two ways at once " to be sure that 
each of the two wires accurately bisects 
the star upon which it is set : with a 
double-image micrometer, the observer's 
attention is concentrated upon a single 
point without distraction. 

The heliometer is a complete telescope, equatorially mounted, 
and having its object-glass (usually from four to six inches in 
diameter) divided along its diameter, as shown in Fig. 150. 
The semi-lenses are so mounted that they can slide past each 
other for a distance of three or four inches, the distance being 
accurately measured by a delicate scale, which is read by a 
long microscope that comes down through the telescope-tube 
to the eye end. The tube is mounted in such a way that it 
can be turned around in its cradle, so as to make the line of 
division of the lenses lie at any desired position angle. 




414 APPENDIX. [§ 543 

When the two halves of the object-glass are so placed that 
their optical centres, and 1 or and 2, coincide, they act as a 
single lens, and form but a single image for each object in the 
field of view : but as soon as they are separated, each half-lens 
forms its own image. The distance between any two objects 
in the field of view is measured by making their images co- 
incide, as indicated in the lower part of the figure, where M 
and S are the images of Mars and of a star, formed by the 
stationary half, B, of the object-glass, which has its centre 
at 0. M ± and S x are the images formed by the other half- 
lens, A, when its centre is 1, and M 2 and S 2 are the images when 
its centre is 2. The distance between the images of S and 
M is therefore either 1 or 2, read off on the sliding scale. 
The direction in which the line 10 2 has to be set to effect the 
coincidence, gives the direction, or position angle, from M to S. 

544. The Transit Instrument. — This instrument has already 
been mentioned, and figured in outline in Art. 58, Fig. 14. It 
consists of a telescope carrying at the eye end a reticle, and 
mounted on a stiff axis that turns in Y's which can have 
their position adjusted so as to make the axis exactly perpen- 
dicular to the meridian. A delicate spirit level, which can be 
placed upon the pivots of the axis to ascertain its horizon- 
tality, is an essential accessory, and it is practically necessary 
to have a graduated circle attached to the instrument in order 
to " set it " for a star, in readiness for the star's transit across 
the meridian. It is very desirable also that the instrument 
should have a " reversing apparatus," by which the axis may 
be easily and safely reversed in the Y ? s. 

The reticle usually contains from five to fifteen vertical 
"wires," crossed by two horizontal ones. Eig. 151 shows the 
reticle of a small transit intended for observations by " eye 
and ear." When the chronograph is to be used, the wires are 
made more numerous and placed nearer together. In order to 
make the wires visible at night, one of the pivots of the in- 



§544] 



THE ADJUSTMENTS OP THE TRANSIT. 



415 



strument is pierced (sometimes both of them) so that the light 
from a lamp will shine through the axis upon a small reflector 
placed in the central cube of the instrument, where the axis 
and the tube are joined. This little reflector sends sufficient 
light towards the eye to illuminate 
the field, while it does not cut off any 
considerable portion of the rays from 
the object. 

The instrument must be thoroughly 
stiff and rigid, without any loose joints 
or shakiness, especially in the mount- 
ing of the object-glass and reticle. 
Moreover, the two pivots must be 
accurately round, without taper, and 
precisely in line with each other, — in 
other words, they must be portions of 

one and the same geometrical cylinder. To fulfil this condi- 
tion, with errors nowhere exceeding yqVtoo" °^ an incn ? taxes 
the highest skill of the mechanician. When accurately con- 
structed and adjusted, the middle wire of the instrument 
always exactly coincides with the meridian, however the in- 
strument may be turned on its axis ; and the sidereal time 
when a star crosses that wire is therefore the star's right 
ascension (Art. 37). 




Fig. 151. — Reticle of the Transit 
Instrument. 



545. The Adjustments of the Transit. — These are four in 
number : 

1. The reticle must be exactly in the focal plane of the object-glass, 
and the middle wire truly vertical. 

2. The line of collimation (i.e., the line which joins the optical 
centre of the object-glass to the middle wire) must be exactly perpen- 
dicular to the axis of rotation. This may be tested by pointing the 
instrument on a distant object, and then reversing the instrument. If 
the adjustment is correct, the middle wire will still bisect the object 
after the reversal. If it does not, the reticle must be set right by 
adjusting screws provided for the purpose. 



416 APPENDIX. [§ 545 

3. The axis must be level. This adjustment is made by the help of 
the spirit-level. One of the Y's has a screw by which it can be slightly 
raised or lowered, as may be necessary. 

4. The azimuth of the axis must be exactly 90°; i.e., it must point 
exactly east and west. This adjustment is made by means of star 
observations with the help of the sidereal clock. Without going into 
detail, we may say that if the instrument is correctly adjusted, the time 
occupied by a star near the pole in passing from its transit across the 
middle wire, above the pole, to its next transit across the same wire, 
below the pole, must be exactly 12 sidereal hours. Moreover, if two 
stars are observed, one near the pole and another near the equator, 
the difference between their times of transit ought to be precisely equal 
to their difference of right ascension. By availing himself of these 
principles, the astronomer can determine the errors of adjustment in 
azimuth and correct them. 

An observation with the instrument consists in noting the 
precise moment by the clock when the object observed crosses 
each wire. The mean is taken to give the time of transit 
across the middle wire. If the " error " of the clock is known 
and the instrument is in exact adjustment, the moment of 
crossing the middle wire will, as already said, give the right 
ascension of the object ; or, if the right ascension of the 
object is already known (if, for instance, the object is an 
"almanac star "), the difference between this and the clock- 
face indication will give the "clock error" (Art. 58). 

546. Astronomical Clock. — Obviously a good clock or chro- 
nometer is an essential adjunct of the transit, and equally so 
of most other astronomical instruments. The invention of the 
pendulum clock by Huyghens was almost as important for the 
advancement of Astronomy as the invention of the telescope 
by Galileo; and the improvement of the clock and chronometer 
in the invention of temperature compensation by Harrison 
and Graham in the 18th century, is fully comparable with the 
improvement of the telescope by the invention of the achro- 
matic object-glass. 



§546] THE CHRONOGRAPH. 417 

The astronomical clock differs in no respect from any other 
clock, except that it is made with extreme care, and has a pen- 
dulum so compensated that its rate will not be sensibly affected 
by changes of temperature. The pendulum usually beats 
seconds, and the clock-face ordinarily has its second-hand, 
minute-hand, and the hour-hand, each moving on a separate 
centre, while the hours are numbered from to 24. 

Excellence in an astronomical clock consists in its maintain- 
ing a constant rate; i.e., in gaining or losing precisely the 
same amount each day ; and for convenience, the rate should 
be small. It is adjusted by raising or lowering the pendulum 
bob, and is generally made less than a second a day. The 
clock error or " correction " can of course be adjusted at any 
time by merely setting the hands. 

The old-fashioned method of time observation consisted 
simply in noting by " eye and ear " the moment (in seconds 
and tenths of a second) when the phenomenon occurred ; as, 
for instance, when a star passed the wire : the tenths, of course, 
were merely estimated, but the skilful observer seldom makes 
a mistake of a whole tenth in his estimation. 

547. The Chronograph. —At present such observations are 
usually made by the help of electricity. The clock is so 
arranged that at every other beat of the pendulum an electric 
circuit is made or broken for an instant, and this causes a 
sudden sideways jerk in the armature of an electric magnet, 
like that of a telegraph sounder. This armature carries a 
pen, which writes upon a sheet of paper moving beneath it. 
The sheet is wrapped around a cylinder six or seven inches 
in diameter, and the cylinder itself turns uniformly once a 
minute : at the same time the pen-carriage is drawn slowly 
along, so that the marks on the paper form a continuous 
spiral, graduated off into two-second spaces by the clock 
beats. When taken off the cylinder, the paper presents the 
appearance of an ordinary page crossed by parallel lines, 



418 



APPENDIX. 



[§547 



spaced off into two-second lengths, as shown in Fig. 152, which 
is a part of an actual record. 



9 h. 35 m. 00.0 s. 



_^_n__TUVUV\AAAAAAAAA/V_ 



Fig. 152. — A Chronograph Record. 




Fig. 153. —A Chronograph by Warner & Swasey. 

The observer at the moment of a star-transit merely presses 
a key which he holds in his hand, and thus interpolates a mark 
of his own among the clock beats on the sheet ; as, for instance, 



§^47] THE MERIDIAN CIRCLE. 419 

at X and Y in the figure. Since the beginning of each minute 
is indicated on the sheet in some way by the mechanism of 
the clock beats, it is very easy to read the time of X and Y\)y 
applying a suitable scale, the beginning of the mark being the 
true moment of observation. In the figure, the initial minute, 
marked when the chronograph was started, happened to be 9 
hours, 35 minutes, the zero in the case of this clock being 
indicated by a double beat. The signal at X, therefore, was 
made at 9 h 35 m 55 s . 45, and that of Y at 9 h 36 m 58 s . 63. The 
" rattle " just preceding X was the signal that a star was 
approaching the transit wire. Fig. 153 is a representation of 
a complete chronograph. 

548. The Meridian Circle. — This has already been briefly 
described in Art. 49, but not in sufficient detail to give much 
real understanding of its construction and appearance. It is 
a transit instrument of large size and most careful construc- 
tion, plus a large graduated circle (or circles), attached to the 
axis and turning with it. The utmost resources of mechanical 
art are expended in graduating this circle with accuracy. The 
divisions are now usually made either two minutes or five 
minutes, and the farther subdivision is effected by the so- 
called " reading microscopes/' four or six of which are always 
used in the case of a large instrument. Since 1" on the cir- 
cumference of a circle is 2-0x2 e "5 P art °^ ^ s rac ^ us ; i* follows 
that on a circle two feet in diameter 1" is only about 17 q 00 of 
an inch. An error of that amount is now very seldom made by 
reputable constructors in placing any graduation line. Fig. 154 
represents a rather small instrument of this kind, having circles 
two feet in diameter, with a four and a half inch telescope. 

Our limits do not permit a description of the reading micro- 
scopes seen at A, B, (7, and D, by means of which the circle is 
read. For these, see works on Practical Astronomy. 

549. Zero Points. — The instrument is used to measure the 
altitude or else the polar distance of a heavenly body at the time 



420 



APPENDIX. 



[§549 



when it is crossing the meridian. As a preliminary, we must 
determine a zero point upon the circle, — the nadir point if we 
wish to measure altitudes or zenith distances, the polar point 
if polar distances or declinations. 




Fig. 154. — A Meridian Circle. 



The polar point is determined by taking the circle reading 
for some star near the pole when it crosses the meridian above 
the pole, and then doing the same thing again twelve hours 
later when it crosses it below. The mean of the two readings, 
corrected for refraction, will be the reading the circle would 



§ 549] COLLIMATING EYE-PIECE. 421 

give when the telescope is pointed exactly to the pole ; tech- 
nically, the "polar point" 

The nadir point is the reading of the circle when the tele- 
scope is pointed vertically downward. It is determined by 
means of a basin of mercury underneath the instrument, the 
telescope being so set that the image of the horizontal wire of 
the reticle, as seen by reflection from the mercury, coincides with 
the wire itself. Since the reticle is exactly in the principal 
focus of the object-glass, the rays emitted from any point in 
the reticle will form a parallel beam after passing through the 
lens, and if this beam strikes perpendicularly upon a plane 
mirror, it will be returned as if from an object in the sky, and 
the lens will re-collect the rays to a focus in the focal plane. 
When, therefore, the image of the central wire of the reticle 
formed by reflection from the mercury coincides with the wire 
itself, we know that the line of collimation of the telescope 
is exactly perpendicular to the surface of the mercury ; i.e., 
precisely vertical. 

550. Collimating Eye-Piece. — To make this reflected image 
visible, it is necessary to illuminate the reticle by light thrown towards 
the object-glass from behind the wires, for the ordinary illumination 
used during observations comes from the op- 
posite direction. This peculiar illumination 
is effected by what is known as the Bohnen- 
berger "collimating eye-piece," shown in Fig. 
155. A thin glass plate inserted at an angle 
of 45° between the lenses of a Ramsden eye- 
piece throws down sufficient light, and yet 
permits the observer to see the wires through 
the glass. FlG - 155 - 

The Collimating Eye-piece. 

Of course the zenith point is just 180° from the nadir point, 
so that the zenith distance of any star is found by merely taking 
the difference between its circle reading (corrected for re- 
fraction) and the zenith reading. 




422 APPENDIX. [§ 550 

Obviously the meridian circle can be used simply as a tran- 
sit, if desired, so that with this instrument and a clock, the 
observer is in a position to determine both the right ascension 
and the declination of any heavenly body that can be seen when 
it crosses the meridian. 

551. There are a number of other instruments which are more or 
less used in special observations. Our space barely permits their 
mention. The principal among them are the so-called "Universal 
Instrument," or Astronomical Theodolite; the " Prime Vertical " in- 
strument (simply a transit faced east and west instead of moving in 
the meridian) ; the " Zenith Telescope " ; and a new instrument by 
Chandler, known as the " Almucantar," which is used to observe the 
time when certain known stars reach a fixed altitude, usually that 
of the pole, an observation from which the time and the latitude of 
the place can be very accurately determined. It is simply a telescope 
carried on a " raft," so to speak, which floats on mercury, the telescope 
being pointed upwards at an angle approximately equal to the latitude 
and keeping automatically ahoays precisely the same elevation. 

552. The Sextant. — All the instruments so far mentioned, 
except the chronometer, require firmly fixed supports, and are 
therefore absolutely useless at sea. The sextant is the only 
one upon which the mariner can rely. By means of it he can 
measure the angular distance between two points (as, for in- 
stance, the sun and the visible horizon), not by pointing first 
on one and afterwards on the other, but by sighting them both 
simultaneously and in apparent coincidence, — a " double-image " 
measurement ; in that respect the sextant is analogous to the 
heliometer. This measurement can be accurately made even 
when the observer has no stable footing. 

Pig. 156 represents the instrument. Its graduated limb is 
usually about a sixth of a complete circle (as its name indi- 
cates) with a radius of from five to eight inches. It is graduated 
in half-degrees which are numbered as whole degrees, and so 
can measure any angle not much exceeding 120°. The index 



§552] 



THE SEXTANT. 



423 



arm, or "alidade," MN in the figure, is pivoted at the centre 
of the arc, and carries a "vernier," which slides along the 
limb and can be fixed at any point by a clamp with an attached 
tangent screw, T. The reading of this vernier gives the angle 
measured by the instrument ; the best instruments read to 10". 
Just over the centre of the arc the " index-mirror," M, about 




Fig. 156. — The Sextant. 



two inches by one and one-half in size, is fastened securely 
to the index-arm, so as to move with it, keeping always per- 
pendicular to the plane of the limb. At H, the "horizon- 
glass" about an inch wide and about the same height as the 
index-glass, is secured to the frame of the instrument in such 
a position that when the vernier reads zero the index-mirror 
and horizon-glass will be parallel to each other. Only half 
of the horizon-glass is silvered, the upper half being left 
transparent. E is a small telescope' screwed to the frame 
and directed towards the horizon-glass. 



424 APPENDIX. [§ 553 

553. If the vernier stands near zero (but not exactly at 
zero) an observer looking into the telescope will see together 
in the field of view two separate images of the object towards 
which the telescope is directed ; and if, while still looking, he 
slides the vernier, he will see that one of the images remains 
fixed while the other moves. The fixed image is formed by 
the rays which reach the object-glass directly through the un- 
silvered half of the horizon-glass ; the movable image, on the 
other hand, is produced by the rays which have suffered two 
reflections, being reflected from the index-mirror to the hori- 
zon-glass and again reflected a second time at the lower half 
of the horizon-glass. When the two mirrors are parallel, the 
two images coincide, provided the object is at a considerable 
distance. 

If the vernier does not stand at or near zero, an observer 
looking at an object directly through the horizon-glass will see 
not only that object, but also, in the same field of view, what- 
ever other object is so situated as to send its rays to the tele- 
scope by reflection from the mirrors ; and the reading of the 
vernier ivill give the angle at the instrument between the tivo 
objects whose images thus coincide; the angles between the 
planes of the two mirrors being just half the angle between 
the two objects, and the half degrees on the limb being num- 
bered as whole ones. 

554. Use of the Instrument. — The principal use of the in- 
strument is in measuring the altitude of the sun. At sea, an 
observer, holding the instrument in his right hand and keep- 
ing the plane of the arc vertical, looks directly towards the 
visible horizon through the horizon-glass (whence its name) at 
the point under the sun ; then by moving the vernier with his 
left hand, he inclines the index-mirror upward until one edge 
of the reflected image of the sun is brought down to touch the 
horizon line. He also notes the exact time by the chronom- 
eter, if necessary. The reading of the vernier, after due 






§554] 



USE OF THE SEXTANT. 



425 




correction (Art. 492), gives tlie sun's true altitude at the 
moment. 

On land we have recourse to an "artificial horizon." This 
is merely a shallow basin of mercury, covered with a roof 
made of glass plates having their surfaces accurately plane 
and parallel. In this case, we measure the angle between the 
sun's image reflected in the mercury and the sun itself. The 
reading of the instrument corrected for index-error gives 
twice the sun's apparent altitude. 

The skilful use of the sextant 
requires considerable dexterity, 
and from the small size of the 
telescope the angles measured are 
less precise than those deter- 
mined by large fixed instruments. 
But the portability of the instru- 
ment and its applicability at sea 
render it absolutely invaluable. 
It was invented by Gregory of 
Philadelphia in 1730. 

Fig. 157. — Principle of the Sextant. 

555. The principle that the 
angle between the objects whose images coincide in the sex- 
tant is twice the angle between the mirrors (or between their 
normals) is easily demonstrated as follows (Fig. 157) : — 

The ray SM coming from an object, after reflection first at 
M (the index-mirror) and then at H (the horizon-glass) is 
made to coincide with the ray OH, coming from the horizon. 

From the law of reflection, we have the two angles SMP 
and PMH equal to each other, each being x. In the same way, 
the two angles marked y are equal. From the geometric prin- 
ciple that the angle SMH, exterior to the triangle HME, 
is equal to the sum of the opposite interior angles at H and 
E, we get E = 2 x — 2 y. In the same way, Q = x — y ; whence 
E = 2Q = 2Q'. 



426 



APPENDIX. 



[§556 



THE PYRHELIOMETER. 

556. The pyrheliometer is an instrument devised by Pouillet 
for measuring the amount of heat received from the sun, and he 
made with it, in 1838, some of the earliest determinations of 
the " solar constant." In Fig. 158 aa' is a little snuff-box-like 

capsule, made of thin silver, and con- 
taining 100 grams of water. The bulb 
of a delicate thermometer is inserted 
in the water, and the temperature is 
read at a point m, near the middle 
of the stem. The disc, ss', enables us 
to point the instrument exactly to- 
wards the sun by making the shadow 
of aa' fall concentrically upon it. The 
upper surface of the box is just one 
decimeter in diameter, and is carefully 
coated with lampblack. The instru- 
ment is used by pointing it towards 
the sun, and first holding an umbrella 
over it until the temperature becomes 
stationary or nearly so, after which 
the umbrella is taken away, and the 
sun allowed to shine squarely upon 
the blackened surface for five minutes 
or so, the apparatus being occasionally 
turned on dm as an axis, to stir up the 
water in the box. The rise of temper- 
ature- in a minute would give the solar 
constant directly, were it not for the 
troublesome and uncertain corrections depending upon the 
continually varying absorption of the solar heat by our 
atmosphere. 

For a description of Violles's actinometer (used for the same 
purpose), see " General Astronomy/' Art. 311. 




Fig. 158. 
Pouillet's Pyrheliometer. 



TABLES. 427 

TABLE L — ASTRONOMICAL CONSTANTS. 
TIME CONSTANTS. 

The sidereal day = 23 h 56 m 4 S .090 of mean solar time. 
The mean solar day = 24 h 3 m 56 s . 556 of sidereal time. 

To reduce a time interval expressed in units of mean solar 
time to units of sidereal time, multiply by 1.00273791; Log. of 
0.00273791 =[7.4374191]. 

To reduce a time interval expressed in units of sidereal 
time to units of mean solar time, multiply by 0.99726957 = 
(1 - 0.00273043) ; Log. 0.00273043 = [7.4362316]. 

Tropical year (Leverrier, reduced to 1900), 36p d 5 h 48 m 45 s .51. 
Sidereal year " " " 365 6 9 8.97. 

Anomalistic year " " " 365 6 13 48.09. 

Mean synodical month (new moon to new), 29 d 12 h 44 m 2 S .864. 

Sidereal month, 27 7 43 11.545. 

Tropical month (equinox to equinox) , . 27 7 43 4.68. 
Anomalistic month (perigee to perigee), . 27 13 18 37.44. 
Nodical month (node to node), . . 27 5 5 35.81. 



Obliquity of the ecliptic (Newcomb), 

23° 27' 08".26 - 0".4757 (t - 1900). 

Constant of precession (Newcomb), 

50".248 + 0.000222 (£-1900). 
Constant of nutation (Astron. Conference, 1896), 9".21. 
Constant of aberration (Astron. Conference, 1896), 20".47. 



Equatorial semi-diameter of the earth (Clarke's spheroid of 
1878), — 20 926 202 feet = 6 378 190 metres = 3963.296 mUe8 . 

Polar semi-diameter, — 

20 854 895 feet = 6 356 456 metres = 3949.790 mUe8 . 

Oblateness (Clarke), t^. ¥ ^ ; (Harkness), ^^. 



428 



APPENDIX. 



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430 



APPENDIX. 



TABLE IV. THE PRINCIPAL VARIABLE STARS. 

A selection from S. C. Chandler's third catalogue of variables ("Astronomical 
Journal/' July, L896), containing such as, at the maximum, are easily visible to the 
naked eye, have a range of variation exceeding half a magnitude, and can be Bees 
in the United States. 





Name. 


Place, VMM. 


Range of 
Variation. 


Period (days). 


Remarks. 


o 


a 


8 




1 


R Andromeda) 


h 




in 

18.8 


+ 38' r 


5.6 to 13 




411 


( Mira. Varia- 


2 
3 
4 


oCeti. . . . 
p Persei . . . 
Persei . . . 


2 
2 
3 


14.3 

58.7 

1.6 


3 28 

+ 38 27 
+ 40 34 


1.7 
3.4 
2.3 


9.5 
4.2 
3.5 


2<> 


331.6* 

33 
20* 48'" B5-.43 


j tions in length 
( of period. 
j AUjoL Period 
\ now shortening. 


5 


A Tauri . . . 


3 


55.1 


+ 12 12 


3.4 


4.2 


3<» 


22'' 52"' 12* 


j Algol type, but 


6 


« Auriga) . . 


4 


54.8 


+ 43 41 


3 


4.5 




Irregular 


( irregular. 


7 


a Orionis . . 


5 


49.7 


+ 7 23 


1 


1.6 




196 ? 


Irregular. 


8 


>) Geminorum . 


6 


8.8 


+ 22 32 


3.2 


4.2 




229.1 




9 


£ Geminorum . 


6 


58.2 


+ 20 43 


3.7 


4.5 


lO'i 


3'' 41"' 30 s 




10 


R Canis Maj. . 


7 


14.9 


-16 12 


5.9 


6.7 


l d 


3'' 15"' 58" 


Algol type. 


11 


R Leonis . . 


9 


42.2 


+ 11 54 


5.2 


10 




312.87 




12 


U Hydra) . . 


10 


32.6 


-12 52 


4.5 


6.3 




194 




13 


R Hydra) . . 


13 


24.2 


-22 46 


3.5 


9.7 




425 


Period short'ing 


14 


5 Libra? . . . 


14 


55.6 


- 8 7 


5.0 


6.2 


2<i 


7 1 ' 51"' 22».8 


Algol type. 


15 


R Corona) . . 


15 


44.4 


+ 28 28 


5.8 


13 




Irregular 




16 


R Serpentis . 


15 


46.1 


+ 15 26 


5.6 


13 




357 




17 


a Herculis . . 


17 


10.1 


+ 14 30 


3.1 


3.9 


Two or three inon 


thB, but very irreg. 


18 


U Ophiuchi . 


17 


11.5 


+ 1 19 


6.0 


6.7 




2Qh 7'" 42°.6 




19 


X Boglttarii . 


17 


41.3 


-27 48 


4 


6 




7.01185 




20 


W Sagittarli . 


17 


58.6 


-29 35 


5 


6.5 




7.59445 




21 
22 


R Scuti . . . 
Lyra) . . . 


18 

18 


42.1 
46.4 


- 5 49 
+ 33 15 


4.7 
3.4 


9 
4.5 


12-i 


71.10 
21 »• 47"' 23«.7 


( Secondary mini- 
< mum about mid- 


23 
24 


x cygm . . • 

»j Aquila) . . 


19 
19 


46.7 
47.4 


+ 32 40 

+ 45 


4.0 
3.5 


13.5 
4.7 


7 d 


406 
4h 14m o».0 


( way. 
Period length'ng 


25 


S Sagittie . . 


19 


51.4 


+ 16 22 


5.6 


6.4 


8'» 


9 h 11'" 48\5 




26 


T Vulpeculne . 


20 


47.2 


+ 27 52 


5.5 


6.5 


4.1 


10* 27 m 50" .4 




27 


T Cephei . . 


21 


8.2 


+ 68 5 


5.6 


9.9 




383.20 




•28 


fx Cephei . . 


21 


40.4 


+ 58 19 


4 


5 




432 ? 




29 


8 Cephei . . 


22 


25.4 


+ 57 54 


3.7 


4.9 


5<i 


gh 47m 398,3 




30 


Pegasi . . . 


22 


58.9 


+ 27 32 


2.2 


2.7 




Irregular 




31 


R Cassiopeia) . 


23 


53.3 


+ 50 50 


4.8 


12 




429 





TABLES. 



431 



TABLE V. — STELLAR PARALLAXES AND PROPER MOTIONS 
tademan'fl Table, A«t. Xach., Aug., 18$ 



yo. 


Xa.mk. 


Ma^. 


Proper Motion. 


Annual 
Parallax. 


Distance 
Ligbt Y*€ 


1 


a Centauri . 


' 


.67 


0".75 


4 


2 


LI. 21185 . . 


6.9 


4.75 


0.50 


as 


3 


01 Cygni . 


5.1 


5.16 


0.40 


8 


4 


Sirius . . . 


-1.4 


L31 






5 


1 2398 . . . 




2.40 




9.3 


6 


LI. 9352 . . 


7.5 


0.90 


-■ 


12 


7 


Procyon . . 


0.5 


L25 


".27 


12.3 


8 


LI. 21258 . . 


8.5 


440 


0.20 


12.o 


9 


Altair . . . 


1.0 


0.65 


. 


10.3 


10 


c Indi . 


D.2 


4.60 


0.2" 


10.3 


11 


o 2 Eridani 


4.5 


4.05 


0JL9 


17 


12 


Vega . . . 


2 


0.36 


0.16 


20 


13 


ft Cassiopeia, 


2.4 


5E 


0.10 


20 


14 


" Ophiucni . 


4.1 


L13 


0.15 


21 


15 


* Eridani . . 


4.4 


3.03 


0.14 


23 


16 


AldeVjaran 


1.0 


0.19 


0.12 


27 


17 


pella . . 


0.2 


0.43 


0.11 


29 


18 


Regains . . 


1.4 


0.27 


0.10 


- 


19 


Polaris . . 


2.1 


0.05 


0.07 


47 



These are not all the stars upon Oudeman's list which are given as hav- 
ing parallaxes exceeding 0".l ; but they are probably the best determined 
ones. 



432 



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Letters. 


Name. 


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Name. 


Letters. 


Name. 


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Pj P, Q, 


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B,A 


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K, K, 


Kappa. 


2, <r, s, 


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Delta. 


M, /*, 


Mu. 


Y, v, 


Upsilon 


E, e, 


Epsilon. 


N,v, 


Nu. 


%<t>, 


Phi. 


z,£, 


Zeta. 


«U 


Xi. 


x > x> 


Chi. 


H,7, 


Eta. 


0,0, 


Omicron. 


♦,fc 


Psi. 


©, 6, *, 


Theta. 


II, 7T ? ID 


,pi. 


0, (0, 


Omega. 



MISCELLANEOUS SYMBOLS. 



6 , Conjunction. 
D, Quadrature. 
<? , Opposition. 
Q, Ascending Node. 
?5, Descending Node. 



A.R., or a, Eight Ascension. 
Decl., or 8, Declination. 
X, Longitude (Celestial). 
{I, Latitude (Celestial). 
cf), Latitude (Terrestrial). 



w, Angle between line of nodes and line of apsides ; also 
the obliquity of the ecliptic. 



SUGGESTIVE QUESTIONS. 435 



SUGGESTIVE QUESTIONS 



FOR USE IN REVIEWS. 



To many of these questions direct answers will not be found 
in the book; but the principles upon which the answers depend 
have been given, and the student will have to use his own 
thinking in order to make the proper application. They are 
inserted at the suggestion of an experienced teacher, who has 
found such exercises useful in her own classes. 

1. What point in the celestial sphere has both its right ascension 
and declination zero ? 

2. What are the hour angle and azimuth of the zenith ? 

3. What angle does the (celestial) equator make with the horizon? 
4:. Name the (fourteen) principal points in the celestial sphere 

(zenith, etc.). 

5. What important circles in the heavens have no correlatives on 
the surface of the earth ? 

6. If Vega comes to the meridian at 8 o'clock to-night, at what 
time (approximately) will it transit eight days hence ? 

7. What bright star can I observe on the meridian between 4 and 
5 p.m., in the middle of August? (See star-maps.) 

8. At what time of the year will Sirius be on the meridian at mid- 
night ? 

9. The declination of Yega is 38° 41' ; does it pass the meridian 
north of your zenith, or south of it ? 

10. What are the right ascension and declination of the north 
pole of the ecliptic ? 

11. What are the longitude and latitude (celestial) of the north 
celestial pole (the one near the Pole-star) ? 



436 c APPENDIX. 

12. Can the sun ever be directly overhead where you live? If not, 
why not ? 

13. What is the zenith distance of the sun at noon on June 22d in 
New York City (lat. 40° 42') ? 

14. What are the greatest and least angles made by the ecliptic 
with the horizon at New York ? Why does the angle vary ? 

15. If the obliquity of the ecliptic were 30°, how wide would the 
temperate zone be? How wide if the obliquity were 50°? What 
must the obliquity be to make the two temperate zones each as wide 
as the torrid zone ? 

16. Does the equinox always occur on the same days of March and 
September? If not, why not; and how much can the date vary? 

17. Was the sun's declination at noon on March 10th, 1887, pre- 
cisely the same as on the same date in 1889? 

18. In what season of the year is New Year's Day in Chili? 

19. When the sun is in the constellation Taurus, in what sign of 
the zodiac is he ? 

20. In what constellation is the sun when he is vertically over the 
tropic of Cancer ? Near what star ? (See star-map.) 

21. When are day and night most unequal? 

22. In what part of the earth are the days longest on March 20th? 
On June 20th? On Dec. 20th ? 

23. Why is it warmest in the United States when the earth is 
farthest from the sun ? 

24. What will be the Russian date corresponding to Feb. 28th, 
1900, of our calendar? To May 1st? 

25. Why are the intervals from sunrise to novm and from noon to 
sunset usually unequal as given in the almanac (For example, see 
Feb. 20th and Nov. 20th.) 

26. At what rate does a star change its azimuth when rising or 
setting? (See Arts. 77 and 494, last paragraph.) 

27. Tf the earth were to shrink to half its present diameter, what 
would be its mean density? 

28. Is it absolutely necessary, as often stated, to find the diameter 
of the earth in order to find the distance of the sun from the earth ? 
(See Arts. 127 and 355.) 

29. How will a projectile fired horizontally on tho earth deviate 
from the line it would follow if the earth did not rotate on its axis? 



SUGGESTIVE QUESTIONS. 437 

30. If the earth were to contract in diameter, how would the weight 
of bodies on its surface be affected ? 

31. What keeps up the speed of the earth in its motion around the 
sun? 

32. How many forces are necessary to keep the moon in its orbit? 

33. Why is the sidereal month shorter than the synodic ? 

34. Does the moon rise every day of the month ? 

35. If the moon rises at 11.45 Tuesday night, when will it rise 
next? 

36. How many times does the moon turn on its axis in a year? 

37. What determines the direction of the horns of the moon? 

38. Does the earth rise and set for an observer on the moon ? If so, 
at what intervals ? 

39. How do we know that the moon is not self-luminous? 

40. How do we know that there is no water on the moon ? 

41. How much information does the spectroscope give us about the 
moon ? 

42. What conditions must concur to produce a lunar eclipse? 

43. Can an eclipse of the moon occur in the day-time? 

44. Why can there not be an annular eclipse of the moon ? 

45. Which are most frequent at New York, solar eclipses or lunar ? 

46. Can an occult ation of Venus by the moon occur during a lunar 
eclipse? Would an occultation of Jupiter be possible under the same 
circumstances ? 

47. How much difference would it make with the tides if the moon 
were one-fourth nearer? (Art. 271, note.) 

48. Which of the heavenly bodies are not self-luminous? 

49. When is a planet an evening star ? 

50. What planets have synodic periods longer than their sidereal 
periods? 

51. When a planet is at its least distance from the earth, what is 
its apparent motion in right ascension ? 

52. A planet is seen 120° distant from the sun ; is it an inferior or 
a superior planet ? 

53. Can there be a transit of Mars across the sun's disc? 

54. When Jupiter is visible in the evening, do the shadows of the 
satellites precede or follow the satellites themselves as they cross the 
planet's disc ? 



438 APPENDIX. 

55. Can the transits of Mercury be utilized to determine the dis- 
tance of the sun, like the transits of Venus? 

56. What would be the length of the month if the moon were four 
times as far away as now? (Apply Kepler's third law.) 

57. What is the mass of a planet which has a satellite revolving in 
one-fifth of a lunar month, at a distance equal to that of the moon 
from the earth ? (See Art. 309.) 

58. What is the distance from the sun of an asteroid which has a 
period of eight years ? 

59. How much would the mass of the earth need to be increased to 
make the moon at its present distance revolve in one-fourth its present 
period? (See Arts. 309 and 508.) 

60. Upon what circumstances does the apparent length of a comet's 
tail depend ? 

61. How can the distance of a meteor from the observer, and its 
height above the earth, be determined ? 

62. What heavenly bodies are not included in the solar system ? 

63. How do we know that stars are suns? How much is meant by 
the assertion that they are? 

64. Suppose that in attempting to measure the parallax of a bright 
star by the differential method (Art. 522) it should turn out that the 
small star taken as the point to measure from, and supposed to be far 
beyond the bright one, should really prove to be nearer. How would 
the measures show the fact ? 

65. If a Centauri were to travel straight towards the sun with x 
uniform velocity equal to that of the earth in its orbit, how Jong 
would the journey take, on the assumption that the star's parallax 
is 0".75? 

66. If Altair were ten times as distant from us, what would be its 
apparent " magnitude " ? What, if it were a thousand times as 
remote? (See Arts. 436, 437; and remember that the apparent; 
brightness varies inversely with the square of the distance.) 



SYNOPSIS FOR REVIEW AND EXAMINATION. 



This synopsis is intended to facilitate the work of teacher 
and pupil in reviews and in preparation for examination. 

A student who has been reasonably faithful in the original 
class work generally needs, in review, to look up only a com- 
paratively small proportion of the topics he has studied ; the 
difficulty is to know beforehand just what those topics are 
without going over the whole ground. 

By an intelligent use of the synopsis he will be able at 
once to discriminate those with respect to which his memory 
and understanding are clear from those with respect to which 
he is consciously doubtful. He can thus avoid much waste of 
time and labor by confining his attention to the points that 
require it, and in this way will find it possible to deal as 
easily with a review lesson of fifty pages as he could with one 
of half the length without some such guide. The synopsis is 
made very full, and includes references to the appendix as 
well as to the body of the text. Of course it is not expected 
that pupils whose course has been limited to the text will 
look up these appendix articles unless time is specially 
allowed them for the purpose. 

In a few instances, also, topics not mentioned in the book 
at all are introduced (as in article 17), with " teacher's notes " 
added ; in hopes that the instructor will look up some of these 
subjects, and supplement the necessarily scanty information 
of the book. The interest and value of text-book work is 
greatly increased by the occasional introduction of something 
fresh from outside sources. 



440 APPENDIX. 

The numbers refer to articles. Articles numbered above 490 are in the 
appendix. Topics italicized are specially important. 

1. The subject-matter and utility of astronomy, 1-5. Conception 
of the celestial sphere as infinite : the " place " of a heavenly body, 
7-9. Angular measurements and units : relation of the radian to de- 
grees, minutes, and seconds: the number 206264-8, 10, 11. Relation 
between the distance and apparent diameter of a sphere, 12. 

2. Definition of the Zenith (astronomical and geocentric) ; the 
Nadir and the Horizon, 14, 15. The "visible horizon" and dip of 
the horizon, 16. Vertical circles, the Meridian, and parallels of 
altitude, 17, 18. Altitude; Azimuth or "true bearing," 19-22. 

3. Definition of the celestial Poles and the celestial Equator, 26, 
27. Hour-circles and the Meridian, 29, 30. Hour-angle and Declina- 
tion, 31-33. The Vernal Equinox, or First of Aries, 34. Sidereal 
time, 35. Definitions of Right Ascension, 36, 37. Celestial Latitude 
and Longitude, 38, 491. 

4. Relation of the place of the celestial pole to the observer's latitude, 
40. The right, parallel, and oblique spheres, 41-44. 

5. Definitions of the Latitude of a place, 47. Two methods of deter- 
mining the latitude by observation, 48, 51. The Meridian Circle, 49. 
Astronomical Refraction, 50. Variation of Latitude, 71*. 

6. The three kinds of Time — Sidereal, Apparent Solar, and Mean 
Solar — defined as Hour-angles, 53-56. Relative length of the Sidereal 
and Solar Days, 54. The Civil day and the Astronomical day, 57. 
Methods of determining the time, i.e., of finding the " error " of a 
time-piece, 58, 60, 493. The Transit Instrument, 544, 545. The 
Clock, 545. The Chronograph, 546. Personal Equation, 59. 

7. Definitions of the Longitude of a place and its relation to " local 
time," 61. Methods of determining the longitude, (a) by the Telegraph, 
62 ; (I)) by the Chronometer, 63 ; (c) other methods, 64. Local and 
" Standard " times, 65. Beginning of the day, and change of " date " 
when a ship crosses the 180th meridian. 

8. Methods of determining the place of a ship at sea, 67-69. The 
Sextant, 552. Corrections to sextant observations, 492. (Sumner's 
method, teacher's notes.) 

9. Methods of determining the ; * place " of a heavenly body (i.e., 
its right ascension and declination) ; («) by the Meridian Circle, 70; 



SYNOPSIS FOR REVIEW AND EXAMINATION. 441 

(b) by the Equatorial and Micrometer, 71. The Meridian Circle, 
548-550. The Equatorial, 510, 541. The Micrometer, 542. 

10. Principal facts relating to the Earth considered astronomically, 
73. Approximate determination of its form and size, 74, 75. 

11. The Rotation of the Earth : demonstrations of the rotation by 
tfre Foucault pendulum, and other phenomena, 77, 78, 494. Possible 
variability of the rate of rotation, 79. Changes in the position of 
the axis within the Earth, 71*. 

12. Centrifugal force due to the Earth's rotation, and its effect 
upon gravity, 80, 82. Effect in modifying the form of the Earth, 81. 

13. Accurate determination of the dimensions and form of the earth 
by the combination of geodetic and astronomical measurements (measure- 
ments of the length of degrees in different latitudes), 86-89. The 
" oblateness," or " ellipticity," of the Earth (about ^ir)' 90. Station 
Errors, 92. 

14. The form of the Earth determined by pendulum observations, 91. 
Loss of weight between pole and equator, — its amount ( t ^q), and 
explanation, 91. Other methods, 91. Distinction between Astro- 
nomical, Geographical, and Geocentric latitudes, 93, 94. 

15. The Mass and Density of the Earth : definition of mass and 
units of mass, 96, 97. Distinction between mass and weight, 97. 
Measurement of mass without weighing, 496. Scientific units of force, 
the dyne, and megadyne, 97. 

16. The Law of Gravitation: /== G Ml X M \ 99-102. The Con- 

d 2 

stant of Gravitation, and its value (0.000,000,066,6 dynes) in C. G. S. 
system, 101. 

17. Experimental determination of the mass and deiisity of the 
Earth by the Torsion Balance, 104-108. (Other methods, teacher's 
notes.) Mean density of the Earth about 5.55, 107, 108. Central 
density and probable constitution of the Earth's interior, 109. 

18. The Earth's Orbital Motion : The Sun's apparent motion on the 
celestial sphere, 110, 111. The Ecliptic, Equinoxes, and Solstices, 112, 
113. The Zodiac and its signs, 114. 

19. The Earth's orbit, distinguished from the Ecliptic, 115. Method 
of finding the form of the Earth 1 's orbit, 115, 116. Definitions of peri- 
helion and aphelion ; semi-major axis, radius-vector, and eccentricity; 



442 APPENDIX. 

anomaly, 117. Law of the orbital motion (equal areas), 118. Changes 
in the orbit : secular constancy of major axis and period ; oscilla- 
tion of inclination and eccentricity, 120. 

20. Precession of the Equinoxes : the phenomenon itself and its dis- 
covery, 122. Elfect upon the place of the pole among the stars, 123. 
Physical explanation, 124. (Illustration by gyroscope, teacher's 
notes.) 

21. The Aberration of Light: the phenomenon denned and illus- 
trated, 125. Effect upon the place of a star, 126. Determination of 
the Sun's distance by means of aberration, 127. 

22. Apparent and Mean Solar time, 128. The Equation of time, 
128, 497-499. 

23. The Seasons, 129-132. 

24. The three kinds of year, Sidereal, Tropical, and Anomalistic, 
124. The Julian and Gregorian Calendars, 134-138. The Metonic 
Cycle, 135. 

25. The Moon : her apparent motion in the heavens, 140. Defini- 
tions of Conjunction, Opposition, Syzygy, and Quadrature, 140. 
The Sidereal and Synodic months, and the relation between them 

( — = — — r=, ), 141. The Moon's path among the stars ; its inclina- 
tion ; the nodes and their regression, 142. Interval between transits, 
etc., 143. Harvest and hunter's moon, 144. The Moon's orbit, and 
method of finding its form, 145. Definitions of perigee, apogee, and 
apsides, 145. 

26. Parallax (geocentric and heliocentric) defined, 146, 147. Hori- 
zontal parallax, 147. Relation between the horizontal parallax of a body 

206265 > 



and its distance, I R = i — ), 148. 

27. A method of finding the Moon's distance and parallax, 149. 
(Other methods, teacher's notes). The result: mean distance of 
Moon = 60.3 times the radius of the Earth, or 238,840 miles, 150. 
Variation of distance, 150. Form of Moon's path relative to the 
Sim, 150. 

28. The Moon's diameter, area of surface, and volume, 152. Her 
mass, density, and surface-gravity, 153. Her axial rotation, 154. 
Librations, 155. (Probable cause of the coincidence of the axial 



SYNOPSIS FOR REVIEW AND EXAMINATION. 44d 

and orbital revolution, teacher's notes ; see also " tidal evolution," 
281). 

29. The Moon's phases, 156. The Terminator and the direction 
of the horns of the crescent, 157. Earth-shine on the Moon, 1§8. 
The Moon's atmosphere, and the probable explanation of its low density or 
absence, 161. Its light and albedo, 162. Heat received from the Moon, 
and probable temperature of its surface, 163, 164. Lunar influences 
upon the Earth, 165. 

30. Character of the Moon's surface, and its telescopic features, 
166-169. Question of Changes now in progress, 172. 

31. The Sun : its parallax and distance, 175. Its diameter, sur- 
face, and volume, 176. Its mass and method of determining it, 178, 
179. Its rotation, 180. The equatorial acceleration, 181. 

32. Methods of studying the solar surface, 182, 183. The photo- 
sphere : its appearance : its constitution as a stratum of cloud, 184, 
222. The faculse, 184. Sun spots : their appearance and nature, 185, 
186. Their dimensions, development, and duration, 187, 188. Their 
distribution and periodicity, 189, 190. Theoretical explanations of sun 
spots, 191. Influence upon the Earth, 192. 

33. The Spectroscope, and its astronomical importance, 193. 
Principles upon which its action depends, 193. Construction of the 
Spectroscope, 194. The Solar spectrum and the Fraunhofer lines, 
194*. 

34. Kirchoff's Laics, 195. Explanation of the Fraunhofer lines, 
195. The " Reversing Layer," 198, 223. Identification of chemical 
elements present in the Sun, 196, 197. Caution as to negative con- 
clusions, 197. 

35. The sun-spot spectrum, 199. Distortion of lines, 200. Dop- 
pler's principle (extremely important), 200, 500. 

36. The Chromosphere and Prominences, 201, 202, 224. Their 
spectrum and discovery of Helium, 202, 202*. Prominences observed 
and photographed with the spectroscope, 203, 501. Different kinds of 
prominences, 204. 

37. The Corona, 205, 206, 225. Its spectrum and " Coronium," 
207. Its nature, 208, 225*. 

38. The Sun's light, 209. Brightness of different parts of its disc, 
210. (Method of measuring the Sun's light, teacher's notes.) 



444 APPENDIX. 

39. The Sun's heat : definition of the " solar constant " and method 
of determining it, 211, 212. The Pyrheliometer, 556. The solar radi- 
ation expressed in terms of melting ice, 213; in terms of energy, 214. 
Radiation at the Sun's surface, 215. The question of the Sun's tem- 
perature, 216, 217. Constancy of the solar radiation, 218. Helm- 
holtz's theory of its maintenance by slow contraction, 210. Age and 
duration of the Sun, 220. 

40. Summary of received theories as to the constitution of the 
Sun, 221-225*. 

41. Eclipses : dimensions of the Earth's shadow, 227. The pe- 
numbra, 228. Lunar eclipses, their cause and varieties, 229. Dura- 
tion, 230. Lunar ecliptic limit, 231. Phenomena of a lunar eclipse 
and explanation of the Moon's ruddy illumination during eclipse, 
232. 

42. Solar eclipses : dimensions of the Moon's shadow, especially its 
length, compared with the distance of the Moon from the Earth, 231. Ex- 
planation of total, annular, and partial eclipses, 235, 236. Velocity 
of the shadow over the Earth's surface and duration of the different 
kinds of solar eclipses, 237. Phenomena of a total solar eclipse. 239. 

43. The solar ecliptic limits, 238. Number of eclipses (both solar 
and lunar) in a year, 242. Frequency of various kinds of eclipses, 
243. Recurrence of eclipses : the Saros, 244. Occnltations of stars, 
245, 246. 

44. Celestial mechanics : motion of a body not acted on by any 

force, 247. Motion under the action of a force, 248. "Law of equal 

areas" etc., when the force is central, 249, 502. The case of motion in 

/ 47r 2 r\ 
a circle ( f= J , 250. Kepler's Laws, 251-253, 503. Inferences 

front those laws, 254. 

45. Newton's verification of the hypothesis of gravitation front the 
motion of the Moon, 255, 505. 

46. The conies, 257, 506. " The problem of two bodies" 258, 259. 
The criterion which determines the species of the orbit, 259, 507*. The 
" parabolic velocity," or "velocity from infinity. " 507*. Intensity 
of the Sun's attraction on the Earth, 260. 

47. The "problem of three bodies," as yet solved only for special 
cases, 261. The "disturbing force " only a small component of the 



SYNOPSIS FOR REVIEW AND EXAMINATION. 445 

attraction of the disturbing body, 26*2. " Perturbations," and the 
"instantaneous ellipse," 263, 264. Lunar perturbations due only to 
action of the Sun. 265. 

48. The tides : the phenomenon itself, 266. Definition of technical 
terms, flood and ebb, spring and neap, etc., 267. The tide-raking 
force explained, 268-271. Relative efficiency of the Sun and Moon, 
271. 

40. Motion of tides as it would be if the Earth were a liquid globe, 
272. High water then 90° from Moon, 272. Free and forced oscilla- 
tions, 273. Cotidal lines and actual course of tide-wave, 274, 275. 
Height of tides under various circumstances, 277-279. 

50. Theoretical effect of tides on the Earth's rotation, 280. Effect 
on Moon's motion, 281. Tidal evolution, 281. 

51. The planets : their names, approximate periods and distances 
from the Sun : Bode's Laic, and its failure in the case of Neptune, 
282-285. 

52. Definition of sidereal and synodic periods, and the relation 
between them. 286. 

53. The general law of relative motion, and the apparent epicycloidal 
motion of planets with reference to the earth, 287, 288. Definitions 
of terms, opposition, elongation, etc., 289. 

54. The apparent alternate direct and retrograde motions of the 
planets in Longitude and Right ascension, 290. Motion in Latitude, 
293. 

55. Motions of the planets with respect to the Sun's place in the 
sky, i.e., in " elongation " : difference between superior and inferior 
planets in this regard, 291, 292. 

56. The Ptolemaic and Copernican systems, 294, 295. (The 
Tychonic system, teacher's notes.) 

57. The " elements " of a planet's orbit, 296, 507. 

58. Observations necessary for their determination, 296. (How to 
determine a planet's place at a given moment from observations made 
for several days about that time : interpolation of observations, teach- 
er's notes.) 

59. Method of determining the period of a planet, 297. 

60. Geometrical method of determining a planet's distance from the Sun 
in astronomical units, 298-301. 



446 APPENDIX. 

61. Planetary perturbations : periodic and secular, 302-304. 
Effect of secular perturbations on major axes and periods, on inclina- 
tions and eccentricities, on nodes and lines of apsides, 304. Sta- 
bility of the system, 305. 

62. Method of finding the diameter, surface, and volume or bulk of 
a planet, 307, 308, 542. 

63. Determination of the mass of a planet, 309, 508 ; of its density 
and surf ace-gravity, 309. 

64. Determination of a planet's axial rotation and other data 
connected with it, 310. 

65. Physical data characteristic of the planet, 311. Satellite sys- 
tems, 312. Relative accuracy of different data, 314. 

66. Humboldt's Classification of the planets and the leading character- 
istics of each class, 313. 

67. Mercury : peculiarities of its orbit, 316, 317. Its magnitude, 
mass, and density, 318. Telescopic appearance, phases, atmosphere, 
and albedo, 319. Its axial rotation, 319. Transits, 326, 327. 

68. Venus: peculiarities of its orbit, 321, Magnitude, mass, density, 
etc., 322. Brightness, phases, atmosphere, etc., 323, 324. Surface 
markings and axial rotation, 325, 325*. Transits, 326, 327. 

69. Mars : peculiarities of its orbit, 328. Magnitude, mass, density, 
and surface gravity, 329. General telescopic aspect,*phase, atmosphere, 
albedo, 330. Axial rotation, 331. Surface markings, canals and 
their gemination, seasonal changes, 332, 333*. Maps of the planet, 
334. Temperature, 335. Satellites, 336. Habitability, 337. 

70. The asteroids : their discovery and nomenclature, 338. Their 
orbits, 339. Their number, size, and probable aggregate mass, 340. 
Their probable origin, 341. 

71. Possible intra-mercurial planets, 342. The Zodiacal light, 
313. 

72. Jupiter : its orbit and period, 344. Its magnitude, mass, and 
density, 345. Telescopic appearance, albedo, atmosphere, etc., 346, 
317. Axial rotation, 348. Surface markings (belts, red spot, etc.), 
probable temperature and physical condition, 346, 349. Its satellites 
and the phenomena they present, 350, 351. Discovery of the fifth 
satellite, 350. 

73. The "Equation of light" defined, 352. Value of the " Constant 



SYNOPSIS FOR REVIEW AND EXAMINATION. 447 

of the light equation " (499 s ) and its determination by means of the 
eclipses of the Jupiter 9 s satellites, 352-354. Determination of the Sun's 
distance by this means, 355. (How the velocity of light is measured, 
teacher's notes.) 

74. Saturn : its orbit, 356. Dimensions, mass, density, surface- 
gravity, and rotation, 357. Surface markings, albedo, and spectrum, 
358. Its rings, discovery, dimensions, phases, and periodic disappear- 
ance, 360. Their constitution and structure, 361. Keeler's spectro- 
scopic demonstration of the relative rate of rotation of the outer and inner 
edges of the ring, 361. Its satellite system, 362. 

75. Uranus : its discovery by Herschel, 363. Orbit and period ; 
diameter, mass, and density ; albedo, color, and spectrum, 363. Its 
satellites and the peculiarity of their orbital motion, 364. 

76. Neptune : its discovery, by Leverrier, Adams, and Galle, 365, 
366. Its orbit and period; diameter, mass, and density ; albedo and 
spectrum, 367. Its satellite, 368. The Sun and solar system as seen 
from Neptune, 369. Possible ultra-neptunian planets, 370. 

77. Comets : their general aspect, numbers, and designation, 371, 
372. Brightness and duration of visibility, 373. Their orbits, and 
the relative number of hyperbolas, ellipses, and parabolas, 374, 375. 
Comets as "visitors," 379. 

78. Elliptic comets, and the relation between the short-period comets 
and Jupiter, 376. Comet "families," 392. Comet " groups," 377. 
The "Capture theory," 392. Comet 1889 V. (at one time called the 
Lexell Brooks Comet) as illustrating this theory, 399*. 

79. Physical characteristics of comets : their constituent parts 
(coma, nucleus, tail, etc.), 381. Dimensions and change of dimen- 
sions, 382. Mass and density of comets, 383, 384. Character of their 
light and its spectrum ; presence of carbon and hydrogen, 386. Phe- 
nomena in the head of a comet which accompany approach to the Sun, 
387. The tail and its formation, 388, 389. Anomalous phenomena, 
390, 399. Nature of comets, 391. Remarkable comets, 394-399*. 
Photography of comets, 399**. Danger from comets, 509. 

80. Meteorites : circumstances of their fall, 400. Their number, 
size, and constitution (stones and irons), 401. Path, velocity, etc., 
402. Method of observation, 403. Explanation of their light and 
heat, 404. Their probable origin, 405. 



448 APPENDIX. 

81. Shooting stars : their nature and number ; difference between 
hourly number in evening and morning, 406, 407. Elevation, path, and 
velocity, 408. Brightness, material, probable mass, etc., 409, 410. 
Insignificance of effects due to their fall on the Earth, 411. 

82. Meteoric showers : general character of the phenomenon ; 
" the radiant" 412. Explanation of such showers and the fixity of 
date, 413. Designation and peculiarities of different meteoric swarms, 
412, 413. The Mazapil meteorite, 414. The connection between comets 
and meteoric showers, 415-417. Lockyer's " meteoritic hypothesis," 
418. 

83. The fixed stars: their nature and 'number, 419, 420. The 
constellations, 421. Names and designations, 422. Star catalogues 
and charts, 423-125. Stellar photography, 425. 

84. Star motions : common motions and proper motions; maximum 
and ordinary amounts of proper motion, 426, 427. Relation of a star's 
proper motion to its real motion, 428. Radial motion (aj>proach or 
recession) measured by the spectroscope, 429, 500. Motion of the Sun in 
space (the " Sun's way "), 430. 

S^>. Distance of the stars : heliocentric, or annual, parallax and its 
relation to the star's distance, 431. Principle on which measurement of 
stellar distances depends, 432. Methods of measuring stellar parallax, 
— the absolute method, 521 ; the differential, 522. (Method by spectro- 
scopic observations on a binary star, teacher's notes). The " Light- 
year" as the unit of stellar distance, 433. 

86. Light of the stars: star magnitudes, 434, 435. The "light- 
ratio," and " absolute " scale of magnitudes, 436, 437. Relation between 
size of telescope and smallest magnitude visible with it (mag. 
= 9 + 5 X log- of diameter of object glass in inches), 438. Starlight 
compared with sunlight, 440, 441, 443. Why stars differ in <>rightness, 
444. Heat from the stars, 442. Size of stars (case of Algol), 445. 

87. Variable stars: different classes, 446-448. Temporary stars or 
u Novce," 450. Periodic stars of the " Mira " type, 451. Short-period 
variables of P Lyrm type, 452. The " Algol " type, 453. Explanations 
of variability : gaseous eruptions, meteoritic collisions, eclipses, 454. 
454*. Number and designation of variables, 455. Variable-star 
clusters, 455*. 

88. Star-spectra : early work and identification of chemical ele- 



SYNOPSIS FOtt REVIEW AND EXAMINATION. 449 

ments present in stars, 456. Secchi's classification of stellar spectra, 
457. Photography of stellar spectra : the " slitless " spectroscope, its 
advantages and disadvantages, 458, 459. Scintillation of the stars, 
460. 

89. Double and multiple stars, their number, color, etc., 461. Dis- 
tance and position angle, 461, 542. Distinction between pairs optically 
and physically double, 462. Binary stars and the nature of their 
orbits, 463, 464. Dimensions and periods of their orbits, 465. (Pos- 
sible spectroscopic determination of the actual size of the orbit and 
so of the distance of the pair from the Sun, teacher's notes.) Spec- 
troscopic binaries (detected by shift of lines or by doubling of lines), 
465*. Masses of binary stars, how determined, 466. Evolution of 
binary systems, 466*. Question of planets attending stars, 467. 

90. Multiple stars, 468. Star clusters, the Pleiades, etc.. 469, 
455*. Probable distance of clusters and size of the stars that com- 
pose them, 469. 

91. The nebulae : number and general characteristics, 470. Forms 
of nebula?, variability of some, drawings and photographs, 470, 471. 
Changes in them, 472. Their characteristic spectrum and its evidence 
as to their constitution, and essential difference from clusters, 473. 
Motions of approach and recession, 473*. Distance and distribution 
of nebula?, 474. 

92. Distribution of stars in the heavens : the galaxy, 475. " Star 
gauges " and relation of stars to the plane of the galaxy, 476. Distri- 
bution of stars in space, the stellar universe, 477, 478. Question of 
a " stellar system " : no central Sun, 479, 480. 

93. Cosmogony : general considerations, 481, 482. Statement of 
Laplace's "nebular hypothesis, 9 ' 483. Necessary modifications, 484. 
(Difficulties from retrograde revolution of satellites of Uranus and 
Neptune, and possible explanations, teacher's notes.) Tidal evolu- 
tion, 281, 466* (and teacher's notes). Lockyer's " meteoritic 
hypothesis," 485. 

94. Bearing of the theory of heat upon theories of cosmogony, 
487, 488. Indications as to the age and duration of the system, 
489. The " dissipation of energy and non-eternity of the present 
system, 490. 

95. Methods of determining the parallax and distance of the Sun : 



450 APPENDIX. 

General and historical remarks, 510, 511. Classification of methods, 
as geometrical, gravitational, and physical, 512. 

96. Geometrical methods : Observations of Mars near opposition 
from two or more widely separated stations, 514. From a single equa- 
torial station, 515. Parallax from observations of the nearer asteroids, 
515. By transits of Venus : Halley's method, 517. De F Isle's method, 
518. Heliometric and photographic observations, 519. 

97. Gravitational methods : the " parallactic inequality " of the 
Moon, 520. Perturbations of Mars and Venus by the Earth, 520. 

98. Physical methods : " aberration " and the velocity of light, 
127. The velocity of light and the equation of light, 355. 

99. The telescope : simple refracting, 530. Magnifying power and 
brightness of image, 531, 532. The achromatic object glass, 533, 534. 
Diffraction and " spurious discs," 534*. Eyepieces, positive and 
negative, 535. The reflecting telescope : various forms, 537. Rela- 
tive advantages of refractors and reflectors, 539. Great telescopes, 
538. The equatorial mounting, 540, 541. 

100. The micrometer, 542. The heliometer, 543. The transit 
instrument and its adjustment, 544, 545. The clock and chronograph, 
546, 547. The meridian circle, 548-550. The sextant and the princi- 
ple of its operation, 552-554. 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



A. 

Aberration of light, 125-127 ; of light 
determining distance of sun, 127. 

Absolute scale of star magnitudes, 436. 

Acceleration of Encke's comet, 380; 
of rotation at the sun's equator, 181. 

Achromatic telescope, 533. 

Adams, J. C. (and Leverrier), dis- 
covery of Neptune, 365 ; orbit of the 
Leonids, 415. 

Aerolite. See Meteorite. 

Age of the sun and planetary system, 
220, 489. 

Albedo defined, 162, 311 ; of the moon 
(Zollner), 162; of the planets (Z611- 
ner), 319, 323, 330, 346, 358, 363, 367. 

Algol, or £ Persei, 453. 

Almagest, Ptolemy's, 294. 

Almucantar, Chandler's instrument, 
551. 

Almucantars defined, 18. 

Alphabet, the Greek, page 414. 

Altitude defined, 19; parallels of, 18; 
of the pole equals latitude, 40. 

Amplitude defined, 20. 

Andromeda, nebula of, 470, 471 ; 483 
note; nebula of, temporary star in, 
450. 

Andromedes, or Bielids, 396, 412-414. 

Angular measurement, units of, 10, 11. 

Annual or heliocentric parallax de- 
fined, 147, 431, 432 ; methods of deter- 
mining it for the stars by observa- 
tion, 521-523. 

Annular eclipses, 235. 

/ nomalistic year, 133. 



Anomalous phenomena in comets, 390 ; 

phenomena in occultations of stars, 

246. 
Anomaly defined, 117. 
Apex of the sun's way, 430. 
Aphelion defined, 117. 
Apogee defined, 145. 
Apparent motion of a planet, 287-293; 

motion of the sun, 110; solar time, 

54, 128. 
Apsides, line of, defined, 117; line of, 

of earth's orbit, its revolution, 120; 

of the moon's orbit, 145. 
Arcs of meridian, measurement of* 

86-90. 
Areas, equal, law of, 249. 
Ariel, a satellite of Uranus, 364. 
Aries, first of, defined, 34. 
Asteroids, or minor planets, 338-341 ; 

their probable origin, 341. 
Astronomical constants, table of, page 

409; day, beginning of, 57; latitude, 

distinguished from geographical and 

geocentric, 93, 94 ; symbols, page 414 ; 

unit, — see Distance of the sun. 
Astronomy, subject-matter of, 3; util- 
ity of, 4. 
Atmosphere of the moon, 159 ; of Mars, 

330; of Mercury, 319; of Venus, 324, 

517. 
Attraction of gravitation, its law, 99- 

102 ; solar, on the earth, its intensity, 

260. 
Azimuth defined, 20; determination 

of, 495 ; of a transit instrument, how 

adjusted, 545. 



451 



452 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Balance, torsion, and the mass of the 
earth, 104, 105. 

Bayer, his system of lettering the 
stars, 422. 

Beginning of the century (Ceres dis- 
covered), 338; of the day, 57, 66. 

Bessel, dark stars, 444 ; first measures 
stellar parallax, 521. 

Bethlehem, the star of, 450. 

Biela's comet, 394-396, 416. 

Bielids, or Andromedes, 396, 412- 
414, 416, 417. 

Binary stars, 463-465; their masses, 
466 ; their orbits, 464, 465. 

Bissextile year, 136. 

Bode's law, 284. 

Bond, W. C, discovery of the " gauze 
ring" of Saturn, 359; discovery of 
Hyperion, 362. 

Bredichin, his theory of comets' tails, 
389. 

Brightness of comets, 373; of mete- 
ors, 409 ; of stars, and causes of dif- 
ference, 439-441, 444. 



Cesar, Julius, reformation of the 
calendar, 136. 

Calendar, the, 134-138. 

Calory, the, denned, 211. 

Canals of Mars, 333. 

Capture theory of comets, 393, 

Cardinal points denned, 30. 

Cassegrain, his form of reflecting 
telescope, 537. 

Cassini, J. D., discovers division in 
Saturn's ring, 359; discovers four 
satellites of Saturn, 302. 

Catalogues of stars, 423. 

Cavendish, his experiment for rind- 
ing the earth's density, 104, 105. 

Celestial globe described, 524-528: 
sphere, infinite, 7. 

Central force, motion under it, 249, 
250, 502. 

Centrifugal force due to earth's rota- 
tion, 80-82. 

Ceres, the first of the asteroids, 338. 



Chandler, S. C, his almucantar, 551 ; 
his catalogue of variable stars, 455. 

Changes, gradual, in the brightness 
of stars, 447; on the surface of the 
moon, 172. 

Chemical constitution of the sun, 196- 
198. 

Chromosphere of the sun, 201, 224; 
and prominences, how made visible 
by the spectroscope, 501. 

Chronograph, the, 547. 

Chronometer, longitude by, 63, 69; 
rate and error of, 58, 546. 

Circle, meridian, the, 548-550. 

Circles, hour, defined, 29. 

Circular motion under central force, 
250. 

Circumpolar stars, latitude by, 48. 

Civil day and astronomical day, 57. 

Classification of the planets, Hum- 
boldt, 313 ; of stellar spectra, Secchi, 
457 ; of variable stars, 446. 

Clock, the astronomical, 546; its rate 
and error, 58, 546. 

Clusters of stars, 469. 

Collimating eye-piece, 550. 

Collimation, line of, 545. 

Comet, Biela's, 394-396, 416; Donatio, 
371, 387 ; Encke's, 376, 380 ; Halley 's, 
376; of 1882,397-399. 

Comets, anomalous phenomena shown 
by, 390; attendant companions, 399 ; 
brightness and visibility, 373; cap- 
ture theory of their origin, 393 ; cen- 
tral stripe in tail, 390 ; connection 
with meteors, 415-417; constitution 
of, 381, 391; danger from, 509; den- 
sity of, 384 ; designation and nomen- 
clature, 372; dimensions of, 382; el- 
liptic, 376; envelopes in head, 381, 
387; families of, 392; formation of 
the tail, 388; general features of, 
371 ; their light and spectra, 386 ; 
mass of, 383 ; nature of, 391 ; num- 
ber of, 371 ; orbits of, 374, 375 ; peri- 
odic, their origin, 392; sheath of 
comet of 1882, 399; tails or trains, 
388, 389 : visitors to the solar system, 
379. 



INDEX. 



453 



[All references, unless expressly stated to 

Comet-groups, 377. 

Common, A. C, photographs of the 

moon, 174. 
Conic sections, the, 257, 506. 
Conjunction defined, 140, 289. 
Constant, solar, defined and discussed, 

211, 212. 
Constellations, the, 421. (For detailed 

description see " Uranography.") 
Constitution of comets, 381; of the 

sun, 221-225. 
Contraction of a comet nearing the 

sun, 382; of the sun, Helmholtz's 

theory, 219. 
Copernicus, his system, 295. 
Correction or error of a time-piece, 58, 

546. 
Corrections to a measured altitude, 

492. 
Corona, the solar, 205-208, 225. 
Coronium, hypothetical element of the 

corona, 207, 225. 
Cosmogony, 481-488. 
Cotidal lines, 274. 
Cycle, the Metonic, 135. 

D. 

Dark stars, 444, 464. 

Darwin, G. H., demonstrates that a 
meteoric swarm behaves like a gas- 
eous nebula, 485 ; tidal evolution, 281. 

Day, beginning of, 66 ; civil and astro- 
nomical, 57. 

Declination defined, 31; determined 
by the meridian circle, 70; parallels 
of, 28. 

Deferent defined, 294. 

Deimos, a satellite of Mars, 336. 

De l'Isle, his method of observing a 
transit of Venus, 518. 

Density of comets, 384; of the earth, 
its determination, 107, 108; of the 
moon, 153; of the sun, 178. 

Designation and nomenclature of 
comets, 372; and nomenclature of 
the stars, 422 ; and nomenclature 
of variable stars, 455. 

Diameter of a planet, how determined, 
307. 



the contrary, are to articles, not to pages.] 

Disc, spurious, of a star, 534. 

Difference of brightness in stars, its 
causes, 444. 

Diffraction, telescopic, 534*. 

Diffraction grating, the, 193. 

Dimensions of the stars, 445. 

Dione, a satellite of Saturn, 362. 

Dip of the horizon, 16, 492. 

Displacement of spectrum lines by 
motion in line of sight, 200, 429, r>00. 

Distance of a body as depending on 
its parallax, 148; of the nebula?, 
474; of a planet from the sun, how 
determined, 298-300; of the stars, 
432, 433; of the sun, by aberration 
of light, 127; of the sun, by the equa- 
tion of light, 355; of the sun, by its 
parallax, 513-520. 

Distribution of the nebulae, 474; of 
the stars in the heavens, 476; of sun 
spots, 190. 

Disturbing force, the, 262. 

Diurnal or geocentric parallax defined, 
147; rotation of the heavens, 23, 
24. 

Doppler's principle, 200, 429, 500. 

Double stars, 461-466; measurement 
of, 461; optical and physical, dis- 
tinguished, 462. 

Draper, H., photograph of the nebu- 
la of Orion, 471 ; photographs of star 
spectra, 458. 

Duration of solar eclipses, 237 ; prob- 
able, of the solar system, 489. 



Earth, the, astronomical facts relating 
to it, 73; its density, 103-108 ; dimen- 
sions of, 74, 75, 84, Table I.; ellip- 
ticity or oblateness determined, 
85-91; its interior constitution, 109; 
mass determined, 103-108; orbital 
motion of, 110-118; its orbit, changes 
in, 120; its rotation affected by the 
tides, 280; its rotation, proofs of, 76- 
78; shadow of , its dimensions, 227: 
surface area and volume, 95 ; veloci- 
ty in its orbit, 175. 

Earth-shine on the moon, 158. 



454 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages. 1 



Eastward deviation of falling bodies, 
78. 

Ebb defined, 267. 

Eccentricity of a conic, 257; of the 
earth's orbit, 116, 117; of the earth's 
orbit, variation of, 120; of an ellipse 
defined, 117, 257. 

Eclipses, frequency of, 243; of Jupi- 
ter's satellites, 351-354 ; lunar, 229 ; 
Oppolzer's canon of, 241 ; number i:i 
a year, 242 ; recurrence of, 24 1 ; so- 
lar, duration of, 237; solar, phenom- 
ena of, 239; solar, varieties of, total, 
annular, and partial, 235, 236. 

Ecliptic, the, defined, 112; obliquity 
of, 112; poles of, 113; variation of its 
obliquity, 120. 

Ecliptic-limits, lunar, 231 ; solar, 238. 

Effect of tides on the rotation of the 
earth, 280. 

Effects of meteors and shooting stars, 
411; of wind and barometric pres- 
sure on the tides, 278. 

Elements, chemical, recognized in the 
stars, 456; chemical, recognized in 
the sun, 197 ; of a planet's orbit, 296, 
507; of the planets, Table II., page 
410. 

Ellipse, the, defined and described, 
117,257. 

Elliptic comets, 376. 

Ellipticity, or oblateness, of the earth 
defined, 90; of the earth measured, 
89-91. 

Elongation defined, 140, 289. 

Enceladus, a satellite of Saturn, 362. 

Encke, J. F., his value of the solar 
parallax, 511. 

Encke's comet, 376, 380. 

Energy of the solar radiation, 214, 
215. 

Enlargement, apparent, of the discs 
of sun and moon near the horizon, 
11, note. 

Envelopes in the head of a comet, 381, 
387. 

Epicycle defined, 294. 

Equation of light, 352, 353; personal, 
59; of time, 128, 497^99. 



Equator, celestial or equinoctial, de- 
fined, 27. 

Equatorial acceleration of the sun's 
surface rotation, 181; instrument, 
the, 540, 541 ; use in determining the 
place of a heavenly body, 71. 

Equinoctial, the, or celestial equator, 
defined, 27. 

Equinox, vernal, defined, 34. 

Equinoxes, precession of, 122-124. 

Erecting eye-piece, 535. 

Error or correction of a timepiece, 58, 
546. 

Eruptive prominences on the sun, 204. 

Establishment of a port, 267. 

Evolution, tidal, 2^1. 

Eye-piece, colliinating, 550; solar, or 
helioscope, 182. 

Eye-pieces, telescopic, various forms, 
535. 

K. 

Faculse, solar, 184. 

Families of comets, 392. 

Filar micrometer, the, 542. 

Flood tide, 267. 

Force, disturbing, the, 262; units of, 
distinguished from mass-units, 97. 

Form of the earth's orbit determined, 
116. 

Foucault, his gyroscope experiment, 
78; his pendulum experiment, 77, 
494 ; theory of the pendulum experi- 
ment, 494. 

Fourteen hundred and seventy-four 
line in the spectrum of the corona, 
207. 

Fhaunhofer lines in the solar spec- 
trum, 196, note. 

Frequency of eclipses, 243. 

G. 

Galaxy, the, 475. 

Galileo, hi.^ discovery of Jupiter's 
satellites, 350; discovery of phases 
of Venus, 321 ; discovery of Saturn's 
ring, 359 ; his telescope, 529. 

Gemination of the canals of Mars, 333. 

Genesis of the planetary system, 482- 
485. 



INDEX. 



455 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 

Geocentric latitude, 94; parallax, 147. 

Geographical latitude, 93. 

Gibbous phase denned, 156. 

Gill, D., his determination of the solar 
parallax, 515. 

Globe, the celestial, described, 524-528. 

Golden number, the, 135. 

Grating, diffraction, 193. 

Gravitation between bodies free to 
move, 102 ; between bodies not free, 
101; proved by Kepler's third law, 
503; statement of the law, 99-102; 
verified by motion of the moon, 255, 
505. 

Gravitational methods of finding the 
solar parallax, 520. 

Gravity distinguished from gravita- 
tion, 83; at the moon's surface, 153; 
at the pole and equator of the earth, 
91 ; at the sun's surface, 179 ; super- 
ficial, of a planet, how determined, 
309. 

Greek alphabet, the, page 414. 

Gregorian calendar, the, 137, 138 ; tele- 
scope, the, 537. 

Groups, cometary, 377. 

Gyroscope illustrating precession, 124 ; 
proving rotation of the earth, 78. 



H. 

Hall, A., determines the rotation of 
Saturn, 357; discovery of the satel- 
lites of Mars, 336. 

Halley discovers the proper motion 
of stars, 427 ; his method of observ- 
ing the transit of Venus, 517; his 
periodic comet, 376. 

Harmonic law, Kepler's, 251-253, 503, 
504. 

Harvest and hunter's moons, the, 144. 

Heat of meteors, its explanation, 404 ; 
from meteors, its total amount, 411 ; 
from the moon, 163, 164; from the 
stars, 442; of the sun, its constancy, 
218; of the sun, its intensity, 217; 
of the sun, its maintenance, 219 j of 
the sun, its quantity, 211. 

Heavenly bodies defined and enumer- 
ated, 2. 



Heliocentric, or annual parallax, de- 
fined, 147, 431. 

Keliometer, the, described, 543 ; used 
in observing the parallax of Mars, 
515 ; used in observing the parallax 
of stars, 522 ; used in observing a 
transit of Venus, 519. 

Helioscopes, or solar eye-pieces, 182. 

Helium, hypothetical element in the 
sun, 202. 

Helmholtz, his theory of the sun's 
heat, 219. 

Herschel, Sir J., illustration of the 
solar system, 315. 

Herschel, Sir W., discovery of two 
satellites of Saturn, 362 : discovery 
of Uranus by, 364; his great tele- 
scope, 538. 

Herschelian telescope, 537. 

Herschels, the, their star-gauges, 
476. 

Hipparchus, 117, 122, 423, 511. 

Horizon defined, rational, sensible, 
and visible, 15, 16 ; dip of, 16, 492. 

Horizontal parallax, 147, 148. 

Hour-angle defined, 32. 

Hour-Circles defined, 29. 

Hourly number of meteors, 407. 

Huggins, W.j observes spectrum of 
*Mars, 330 ; observes spectrum of 
Mercury, 319 ; observes spectrum 
of nebulae, 473; observes spectrum 
of stars, 456 ; observes spectrum of 
temporary star of 1866,450; spectro- 
scopic measures of star motions, 429. 

Humboldt, his classification of the 
planets, 313. 

Hunter's moon, the, 144. 

Huyghens, his discovery of Saturn's 
ring, 359 ; discovery of Titan, 362 ; in- 
vention of the pendulum clock, 546. 

Hyperbola, the, 257, 506. 

Hyperion, a satellite of Saturn, 362. 



Iapetus, the remotest satellite of Sat- 
urn, 362. 

Identification of the orbits of certain 
comets and meteors, 416. 



456 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages. ] 



Illuminating power of a telescope, 

532. 
Illumination of the moon's disc dur- 
ing a lunar eclipse, 232. 
Illustration of the proportions of the 

solar system, olo. 
Inferences from Kepler's laws, 254. 
Influence of the moon on the earth, 

1^5 ; of sun spots on the earth, 11)2. 
Intensity of the sun's attraction on the 

earth, 260; of the sun's heat, 217; 

of the sun's light, 209. 
Intra-Mercurial planets, 342. 
Iron in comets, 386, 398 ; in meteorites, 

401 ; in stars, 456 ; in the sun, 197. 



Janssen (and Lockyer), method of 
observing thj solar prominences, 203. 

Jena, new optical glass made there, 534. 

Julian calendar, the, 136. 

Juno, the third asteroid, 338. 

Jupiter (the planet) , 344, 345 ; his belts, 
red spot, and other markings, 349 ; his 
rotation, 348; his satellites, and their 
eclipses, 350-354. 

Jupiter's family of comets, 376, 392. 

K. 

Kant, a proposer of the nebular hy- 
pothesis, 483. 

Kepler, his laws of planetary motion, 
251-254 ; his third law, correction of, 
504; his third law proving gravita- 
tion, 503. 

Kepler's problem, 119. 

Kirchhoff, fundamental principles of 
spectrum analysis, 195. 



Langley, S. P., observations on the 
moon's heat, 164; observations on 
the sun's heat, 212, note. 

Laplace, his nebular hypothesis, 483- 
488; stability of the solar system, 
305. 

Lass:::.l, his discovery of Ariel and 
[Jmbriel, W4: his discovery (inde- 
pendent) of Hyperion, 362. 



Latitude (celestial) denned and dis- 
cussed, 38, 491 ; (terrestrial), denned, 
40, 47 ; distinction between astro- 
nomical, geographical, and geocentric 
latitude, 93, 94 ; (terrestrial) , length 
of degrees, 89; (terrestrial), methods 
of determining, 48-51, 68. 

Law, Bode's, 284; of the earth's orbital 
motion, 118; of equal areas under 
central force, 249, 502; of gravita- 
tion, 9&-102, 255, 503, 505. 

Laws, Kepler's, 251-253, 502, 503. 

Leap-year, 136, 137. 

Leonids, the, 412, 413, 415-417. 

Leverrier (and Adams), discovery 
of Neptune, 365 ; on the origin of the 
Leonids, 417. 

Librations of the moon, 155. 

Lick telescope, the, 538. 

Light, aberration of, 125-127 ; of com- 
ets, 386; equation of, the, 352, 353; 
of t lie moon, 162; of the sun, its 
intensity, 209, 210; velocity of, used 
to determine the distance of the 
sun, 127, 355; the zodiacal, 343. 

Light ratio of the scale of stellar mag- 
nitude, 436. 

Light year, the, 433. 

Limb defined, 492. 

Limits, ecliptic, the lunar, 231; eclip- 
tic, the solar, 238. 

Local time, 65; time from altitude of 
the sun, 493; time by transit instru- 
ment, 58-60. 

Lockyer, J. N., on cause of sun spots, 
191; on compound character of so- 
called elements, and the reversin ;• 
layer, 197,198; his meteoric hypothe- 
sis, 418, 485; on spectra of comets, 
386 ; on spectra of nebula?, 473 ; (and 
Janssen), spectroscopic method of 
observing the solar prominence's, 
203, 501. 

Longitude and latitude (celestial), 3S, 
491; (terrestrial), denned, 61; (ter- 
restrial), methods of determining it, 
62-64, 69. 

Lunar. See Moon. 



INDEX. 



457 



[All references, unless expressly stated to the contrary, are to articles, not to pages.} 



Magnesium in nebulae (Lockyer) , 473 ; 
in the stars, 456; in the sun, 197. 

Magnifying power of a telescope, 531. 

Magnitudes, star, 434-438; star, abso- 
lute scale of, 436; star, and telescopic 
power, 438. 

Mars (the planet) , 328-337 ; map of 
the planet, 334 and page 230; obser- 
vation for parallax, 514, 515 ; satel- 
lites, 336; Schiaparellis observa- 
tions, etc., 333; telescopic aspect, 
rotation, etc., 330-332. 

Mass, definition, and distinction from 
weight, 96\ 97 ; of comets, 383; of earth, 
103-106; measurement of, in general, 
98; measurement independent of 
gravity, 496; of the moon, 153; of a 
planet, how determined, 309; of a 
planet, formula demonstrated, 508; 
of shooting stars, how estimated, 
410; of the sun determined, 177. 

Masses of binary stars, 466. 

Mazapil, meteorite of, 414. 

Mean and apparent places of stars, 
424 ; and apparent solar time, £5, 128, 
497-499. 

Measurement, angular, units of, 10, 
11; of arcs of latitude, 86-88; of a 
degree by Picard, 255, note. 

Melbourne reflector, 538. 

Mercury (the planet), 316-320; tran- 
sits of, 320. 

Meridian (celestial) defined, 17, 30; 
(terrestrial), arcs of, measured, 86- 
90; circle, the, 49, 548-550. 

Meteoric hypothesis, Lockyer, 418, 485; 
showers, 412, 413. 

Meteorite of Mazapil, 414. 

Meteorites, 400-405; their constitu- 
ents, 401; their fall, 400. 

Meteors, ashes of, 409; connection 
with comets, 415-417 ; heat and light, 
404,411; observation of, 403; origin 
of, 402, 405; path and velocity, 402; 
and shooting stars, their effects on 
the earth, 411. 

Metonic cycle, the, 135. 

Micrometer, the, 542. 



Midnight sun, the, 130. 

Milky Way, the, 475. 

Mimas, the inner satellite of Saturn,362. 

Mira Ceti, 451. 

Missing and new stars, 448. 

Month, sidereal and synodic, 141. 

Months, various kinds, Table I., page 
409. 

Moon, its albedo, 162 ; its atmosphere 
discussed, 159-161; changes on its 
surface, 172; character of its sur- 
face, 167-171; density, 153; diame- 
ter, surface area and bulk, 152; dis- 
tance and parallax, 149, 150; celiacs 
of, 229-233; heat, 163; influence on 
the earth, 165; librations, 155; light 
and albedo, 162; map, 173; mass, 
density, and gravity, 153; motion 
(in general) , 140-145 ; motion affect- 
ed by the tides, 281 ; nomenclature of 
objects on surface, 171, 173; paral- 
lax of, determined, 149, 150; pertur- 
bations of, 265; phases, 156; photo- 
graphs, 174; rotation, 154; shadow 
of, 234; surface structure, 167-171; 
telescopic appearance, 166; tempera- 
ture, 164; water not present, 160; 
verification of gravitation by means 
of its motion, 255, 505. 

Motion, apparent diurnal, of the heav- 
ens, 23-25; of the moon, 140-143; of 
a planet, 287-291; of the sun, 110- 
113; circular, 250; of a free body 
acted on by a force, 247-249; in line 
of vision, effect on spectrum, 200, 
429, 500; of the sun in space, 430. 

Motions of stars, 426^429. 

Mountains, lunar, 167. 

Mounting of a telescope, 540. 

Multiple stars, 468. 

**. 

Nadir defined, 14. 

Nadir-point of meridian circle, 549. 

Neap tide, 267. 

Nebulae, the, 470-474; changes in, 472; 
distance and distribution, 474; spec- 
tra of, 473. 

Nebular hypothesis, the, 483-4S8. 



458 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 

Negative eye-pieces, 535. 

Neptune (the planet), 365-369. 

Newcomb, S., on the age and duration 
of the system, 489; and Michelson, 
the velocity of light, 126. 

Newton, H. A., estimate of the daily 
number of meteors, 407; investiga- 
tion of the orbit of the Leonids, 415 ; 
nature of comets, 391; origin of 
meteors, 402. 

Newton, Sir Isaac, eastward devia- 
tion of falling bodies, 78; law of 
gravitation, 99-102; nature of plan- 
etary orbits, 256-259 ; precession ex- 
plained, 124 ; problem of three bodies, 
261; verification of gravitation by 
the moon's motion, 255, 505. 

Newtonian telescope, 537. 

Nodes of the moon's orbit and their 
regression, 142; of the planetary 
orbits, their motion, 304. 

Nordenskiold, ashes of meteors, 409. 

Number of comets, 371 ; of eclipses in 
a saros, 244; of eclipses in a year, 
242 ; of meteors daily, 407 ; of 
nebulae, 470; of the stars, 420; 
of double-stars, 461. 



Oberon, a satellite of Uranus, 364. 

Oblateness or ellipticity of the earth 
defined, 90. 

Oblique sphere, 43. 

Obliquity of the ecliptic, 112, 120. 

Occultations of stars, 245. 

Olbers, discovers Pallas and Vesta, 
338. 

Oppolzer, his canon of eclipses, 241. 

Opposition defined, 140, 289. 

Orbit of the earth, its form, etc., de- 
termined, 115-118; of the moon, 145, 
151; parallactic, of a star, 432; of a 
planet, its elements, 507. 

Orbital motion of the earth, proof of 
it, 111. 

Orbits of binary stars, 464, 465; of 
comets, 374. 

Origin of the asteroids, 341 ; of mete- 
ors, 402, 405; of periodic comets, 392. 

Oscillations, free and forced, 273. 



Palisa, discovery of asteroids, 338. 

Pallas, the second asteroid, 338, 339. 

Parabola, the, 257, 506. 

Parallax, annual or heliocentric, of the 
stars, 147, 431,432,521-523 ; correction 
for, 492 ; diurnal or geocentric, 147 ; 
in general, defined, 147; (solar), clas- 
sification of methods, 512 ; (solar) , by 
gravitational methods, 520 ; (solar) , 
historical statement, 511 ; (solar) , by 
observations of Mars, 514, 515 ; (so- 
lar) , by physical method, 127, 355 ; 
(solar), by transits of Venus, 516-519 ; 
(stellar), how determined, 521-523. 

Parallaxes, stellar, table of, Table V., 
page 413. 

Parallel sphere, 42. 

Pendulum used to determine earth's 
form, 91 ; Foucault, 77, 494. 

Perigee defined, 145. 

Perihelion defined, 117. 

Period of a planet, how determined, 
297. 

Periods, sidereal and synodic, 141, 286. 

Periodicity of sun spots, 190. 

Periodic perturbations, 303. 

Perseids, the, 412, 416, 417. 

Personal equation, 59. 

Perturbations, general remarks, 263, 
264; lunar, 142, 145, 265; planetary, 
302-304. 

Peters, asteroid discoveries, 338. 

Phase of Mars, 330. 

Phases of Mercury and Venus, 319, 
323; of the moon, 156; of Saturn's 
rings, 360. 

Phobos, a satellite of Mars, 336. 

Photographic power of eclipsed moon, 
232 ; star-charts, 425 ; telescopes, 425, 
534. 

Photographs of the moon, 174; of 
nebulae, 471; of star-spectra, 429, 
458. 

Photography, solar, 183 ; of transit of 
Venus, 519. 

Photometry of star magnitudes, 439, 
440. 

Photosphere, the, 184, 222. 



INDEX. 



459 



[All references, unless expressly stated to the contrary, are to articles, not io pages 



Physical methods of determining the 
sun's parallax, 127, 355. 

Piazzi discovers Ceres, 338. 

Picard measures arc of meridian, 
255, note. 

Pickering, E. C, photographs of star- 
spectra, 458; photometric observa- 
tions of eclipses of Jupiter's satel- 
lites, 354; photometric measures of 
steller magnitudes, 436, 440. 

Place of a heavenly body defined, 9 ; 
of a heavenly body, how determined 
by observation, 70, 71: of a ship, 
how determined, 67-69. 

Planet, albedo of, defined, 311 ; appar- 
ent motion of, 287, 293; diameter 
and volume, how measured, 307 ; dis- 
tance from sun, how determined, 
298-300; elements of its orbit, 507; 
mass and density, how determined, 
309, 508; period, how determined, 
297; rotation on axis determined, 
310; satellite system, how investi- 
gated, 312 ; superficial gravity deter- 
mined, 309. 

Planetary data, their relative accu- 
racy, 314; system, its genesis, age. 
and duration, 482-490. 

Planetoids. See Asteroids. 

Planets, Humboldt's classification, 
313 ; the list of, 282, 283 ; intra-Mer- 
curial, 342 ; minor, 338-341 ; possibly 
attending stars, 467; table of ele- 
ments, Appendix, Table II., page 410 ; 
table of names, symbols, etc., 285. 

Pleiades, the, 469, 471. 

Pogson proposes absolute scale of star 
magnitudes, 436. 

Pointers, the, 23. 

Polar distance defined, 31 ; point of a 
meridian circle, 549. 

Pole (celestial), altitude of, equals lat- 
itude, 40; (celestial), defined, 26; 
(celestial), effect of precession, 123; 
(terrestrial), diurnal phenomena 
near it, 130 ; star, former, a Draconis, 
123; star, how recognized, 23. 

Position angle defined, 461 ; microme- 
ter, 542. 



Positive eye-pieces, 535. 

Pouillet, his pyrheliometer, 556. 

Precession of the equinoxes, 122-124. 

Prime vertical, the, 17. 

Prime Vertical instrument, the, 551. 

Pritchard, his work on stellar pho- 
tometry, 436. 

Problem, Kepler's, 119 ; of three 
bodies, 261-264; of two bodies, 258, 
259. 

Prominences, the solar, 202-204, 224, 
501. 

Proper motion of stars, 427, 428. 

Ptolemaic system, the, 294. 

Ptolemy, 294, 421, 423, 511 

Pyrheliometer, the, 556. 

Q. 

Quadrature defined, 140, 289. 
Quiescent prominences, 204. 

R. 

Radian, the, defined, 11. 

Radiant, the, of a meteoric shower, 

412. 
Radius vector defined, 117. 
Rate of a time-piece defined, 69, 546. 
Rational horizon, 15. 
Rectification of a globe, 528. 
Recurrence of eclipses, 244. 
Red spot of Jupiter, 349. 
Reflecting telescope, the, 537. 
Refracting telescope, the, 530. 
Refraction, astronomical, 50, 492. 
Reticle, the, 536, 544. 
Retrograde and retrogression defined, 

288. 
Reversing layer, 198, 223. 
Rhea, a satellite of Saturn, 362. 
Right ascension defined, 36, 37; how 

determined by observation, 70, 71. 
Right sphere, the, 44. 
Rings of Saturn, the, 359-361. 
Roberts, photographs of nebulae, 471; 
Rosse, Lord, his great reflector, 538; 

observations of lunar heat, 163, 164. 
Rotation, apparent diurnal, of the 

heavens, 23; distinguished from revo- 



4 HO 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



lution, 151, note; of earth, affected 
by tides, 280; of earth, its effect on 
gravity, 80, 81 ; of earth, proofs of, 
76-78; of earth, variability of, 79, 
280; of the moon, 151; of the sun, 
180, 181. 
Rotation-period of Jupiter, 318; of 
Mars, 331; of a planet, how ascer- 
tained, 310; of Saturn, 357. 



Saros, the, 214. 

Satellite system, how investigated, 312 ; 
systems, table of, Table III., page 
411. 

Satellites of Jupiter, 350-354 ; of Mars, 
336; of Neptune, 368; of Saturn, 
362; of Uranus, 364. 

Saturn (the planet), 356-362. 

Scale of stellar magnitudes, 436. 

Schiaparelli, identification of come- 
tary and meteoric orbits, 416 ; obser- 
vations of Mars, 333, 334. 

Schroeter, his observations on Mer- 
cury, 319 ; on Venus, 325. 

Schwabe, discovers periodicity of sun 
spots, 190. 

Scintillation of the stars, 460. 

Sea, position at, how found, 67-69. 

Seasons, explanation of, 129-132. 

Secchi, on stellar spectra, 456, 457; on 
sun spots, 188, 191. 

Secondary spectrum of achromatic 
object-glass, 534. 

Secular perturbations of the planets, 
304. 

Semi-diameter, angular, in relation to 
distance, 12; correction for, 492. 

Sensible horizon, defined, 15. 

Sextant, the, 552-555. 

Shadow of the earth, its dimensions, 
227; of the moon, its dimensions, 
234; of the moon, its velocity, 237. 

Ship at sea, determination of its posi- 

* tion, 67-69. 

Shooting stars (see also Meteors) , 406- 
417; ashes of, 409; brightness of, 
409; effects of, 411; elevation and 
path, 408; mass of, 410; materials 



of, 409; nature of, 406; number, 
daily and hourly, 407; radiant, 412; 
showers of, 412, 413; spectrum of, 
409 ; velocity of, 408. 

Showers, meteoric, 412, 413. 

Sidereal and synodic months, 141 ; and 
synodic periods of planets, 286 ; time 
defined, 35,53; year, 133. 

Signs of the zodiac, 114; effect of pre- 
cession on them, 123. 

Sirius, its companion, 464; light com- 
pared with that of the sun, 440, 443 ; 
its mass compared with that of the 
sun, 465, 466. 

Solar constant, the, 211, 212 ; eye- 
pieces, 182; parallax (see Parallax, 
solar); time, mean and apparent, 
52-56, 497-499. 

Solstice defined, 113. 

Spectroscope, its principle and oon- 
struction, 193, 194; slitless, 458; used 
to observe the solar prominences, 
203, 501; used to measure motions in 
line of sight, 200, 429, 500. 

Spectrum of the chromosphere and 
prominences, 202; of comets in gen- 
eral, 386; of the comet of 1882, 398; 
of meteors, 409; of nebulae, 473; sec- 
ondary, of an object-glass, 534 ; of a 
shooting star, 409 ; of stars, 456-459 ; 
the solar, 196 ; of the solar corona, 
207 ; of a sun spot, 199. 

Spectrum analysis, fundamental prin- 
ciples, 195. 

Speculum of a reflecting telescope, 
537. 

Sphere, celestial, the, 7; doctrine of 
the, 7-45. 

Spots, solar, see Sun spots. 

Spring tide defined, 267. 

Stability of the planetary system, 305. 

Standard time, 65. 

Stars, binary, 4(53-465 ; catalogues of, 
423; charts of, 425; clusters of, 469; 
dark, 444; designation and nomen- 
clature, 422 ; dimensions of, 445 ; dis- 
tance of, 431-433 ; distribution of, 476 ; 
double, 461^66; gravitation among 
them, 462, 464, 479, note ; heat from 



INDEX. 



461 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



them, 442 ; light of certain stars corn- 
pared with sunlight, 440 ; magnitudes 
and brightness, 43 1 - 11 1 ; mean and 
apparent places of, 424 ; missing and 
new, 448 ; motions of, 426-429 ; mul- 
tiple, 468 ; new, 448 ; number of, 420 ; 
parallax of, 431-423, 521-523, Table 
V., page 413; shooting (see Shoot- 
ing stars, also Meteors) ; spectra of, 
456-459; system of the, 479, 480; 
temporary, 450; total amount of 
light from the, 441; twinkling of, 
460; variable, 446-455, Table IV., 
page 412. 

Star -gauges of the Herschels, 476. 

Starlight, its total amount, 441. 

Station errors, 92. 

Stellar parallaxes, table of, Table V., 
page 413 ; photometry, 439-441. 

Structure of the stellar universe, 477- 
480. 

, the, age and duration of, 220 ; ap- 
parent motion in the heavens, 110; 
its chromosphere, 201, 224; its con- 
stitution, 221; its corona, 205-208; 
its density, 178 ; dimensions of, 176 ; 
distance of, 127, 175, 355, Chap. XV.; 
elements recognized in it, 197; fac- 
ulse, 184; gravity on its surface, 
179 ; heat of, quantity, intensity, and 
maintenance, 211-219; light of, its 
intensity, 209, 210; mass of, 177; 
motion in space, 430; parallax of 
(see Parallax) ; prominences, 202- 
204, 224 ; reversing layer, the, 198 ; 
rotation of, 180, 181; spectrum of, 
196 ; temperature of, 216, 217. 

Sun spots, appearance and nature, 
185-188; cause of, 191; distribution 
of, 190 ; influence on the earth, 192 ; 
motions of, 189 ; periodicity of, 190 ; 
spectrum of, 199. 

Superficial gravity of a planet, how 
determined; 309. 

Surface structure of the moon, 167- 
171. 

Swarms, meteoric, 413, 415, 417, 418. 

Swedenborg a proposer of the nebu- 
lar hypothesis, 483. 



System, planetary, its age and dura- 
tion, 489,490; its genesis and evo- 
lution, 482-^85; its stability, 305; 
stellar, its probable nature, 477-480. 

Synodic and sidereal months, 141 ; and 
sidereal periods of planets, 286. 

Syzygy denned, 140. 

X. 

Tables, astronomical constants, Table 
I., page 409 ; astronomical sym- 
bols, page 414; binary stars, orbits 
and masses, 465; Bode's law, 284; 
constellations, showing place in 
heavens, Uranography, page 42; 
Greek alphabet, page 414; moon, 
names of principal objects, 173; plan- 
ets' elements, Table II., page 410; 
planets' names, distances, etc., ap- 
proximate, 285; satellite systems, 
Table III., page 411; stellar paral- 
laxes and proper motions, Table 
V., page 413; variable stars, Table 
IV., page 412. 

Tails of comets, 388, 389. 

Telegraph, longitude by, 64. 

Telescope, achromatic, 533; eye-pieces 
of, 535; general principles of, 529; 
illuminating power, 532 ; magnifying 
power, 531 ; magnitude of stars vis- 
ible with a given aperture, 438; 
mounting of, 540; reflecting, various 
forms, 537; refracting, 530. 

Telescopes, great, 538. 

Temperature of the moon, 164; of the 
sun, 216. 

Temporary stars, 450. 

Terminator, the, defined and described, 
157. 

Tethys, a satellite of Saturn, 362. 

Therm, the smaller unit of heat, 211. 

Thomson, Sir W., the internal heat of 
the earth, 487; the heat of meteors, 
404; the rigidity of the earth, 109. 

Three bodies, problem of, 261-264. 

Tidal evolution, 281. 

Tidal-wave, course of, 275. 

Tide-raising force, 268-27L 



462 



INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Tides, the, definitions relating to, 267 ; 
due mainly to moon's action, 266; 
effect on motion of the moon, 281; 
effect on rotation of the earth, 280; 
effect of wind on time of high water, 
278; height of, 277; in lakes and 
land-locked seas, 279; motion of, 272 ; 
in rivers, 276. 

Time, equation of, 128, 497-499; local, 
from sun's altitude, 493; methods of 
determining, 58-60; sidereal, defined, 
35; solar, mean, and apparent, 54-56, 
128, 497-499; standard, defined, 65. 

Titan, satellite of Saturn, 362. 

Titania, satellite of Uranus, 364. 

Torsion balance used to determine 
earth's mass, 104, 105. 

Total and annular eclipses, 235. 

Trains of meteors, 400, 404. 

Transit or meridian circle, 49, 548-550. 

Transit instrument, the, 58, 544, 545. 

Transits of Mercury, 320; of Venus, 
326,327,516-519. 

Tropical year, the, 133. 

Twilight, 509*. 

Twinkling of the stars, 460. 

Two bodies, problem of, 258, 259. 

Tycho Brahe, his planetary observa- 
tions, 251 ; his temporary star, 450. 

U. 

Ultra-Neptunian planet, 370. 

Umbriel, a satellite of Uranus, 364. 

Universe, stellar, its structure, 477- 
480. 

Uranolith, or Uranolite. See Meteor- 
ite. 

Uranus (the planet), 363-365. 

Utility of astronomy, 4. 

V. 

Vanishing point, 8, 412. 

Variable stars, 446-455; table of, 

Table IV., page 412. 
Velocity, area], angular, and linear, 

502; of earth in its orbit, 175; of 



light, 126; of moon's shadow, 237; 

of meteors and shooting stars, 408 ; 

of star motions, 428, 429. 
Venus (the planet), 321-327; phases of, 

323; transits of, 326, 327, 516-519. 
Vernal equinox defined, 34. 
Vertical circles, 17. 
Vesta, the fourth asteroid, 338. 
Visible horizon defined, 16. 
Vogel, H. C, spectroscopic determina- 
tion of star motions in the line of 

sight, 429. 
Volcanoes on the moon, 168. 
Vulcan, the hypothetical intra-Mercu- 

rial planet, 342. 

W. 

Water absent from the moon, 160, 161. 

Wave-length of a light-ray affected 
by motion in the line of sight, Dop- 
pler's principle, 200, 429, 500. 

Wave, tidal, its course, 275. 

Way, the sun's, 430. 

Weather, the moon's influence on, 165. 

Weight, distinguished from mass, 96, 
97 ; loss of, between pole and equa- 
tor, 91. 

Wolf, diagram of sun-spot periodi- 
city, 190. 

Y. 

Year, the sidereal, tropical, and anom- 
alistic, 133, and Table I., page 409. 



Zenith, the, astronomical and geocen- 
tric, defined, 14. 

Zenith distance defined, 19. 

Zero-points of the meridian circle, 
549. 

Zodiac, the, and its signs, 114; its signs 
as affected by precession, 123. 

Zodiacal light, the, 343. 

Zollxer, determination of planets' 
albedoes, 319, 323, 330, 346, 358, 363, 
367 ; mensnrement of moonlight, 162; 
measures oi light of stars, 440. 



SUPPLEMENTARY INDEX. 



(All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Algol, system of, 454*. 
Arequipa, observations at, 450, 455*, 
465*. 



Bailey, S. I., spectroscopic binaries, 
465* ; variable-star clusters, 455*. 

Barnard, E. E., discovery of a comet 
by photography, 399** ; discovery of 
the fifth satellite of Jupiter, 350; 
measures of asteroids, 340. 

Belopolsky, spectroscopic binaries, 
465*. 

Biliary stars, orbits of, Appendix, 
Table VII. 

Binary systems, evolution of, 466* and 
486, note. 

Boys, Prof. V., determination of the 
"Constant of Gravitation" and of 
the density of the earth, 101, 108. 

C. 

Charlois, photographic discovery of 
asteroids, 338. 

Comet, Holmes', 386, 399*. 

Comets, photographs of, 399**. 

Constant of Gravitation, the, 101. 

Corona, attempted photographs with- 
out eclipse, 225* ; Schaeberle's theory 
of, 225*. 

D. 

)eslandres, H., photography of solar 
prominences, 203. 

dscovery of asteroids, 338 ; of Nep- 
tune, 365 ; of Uranus, 363 ; of satel- 



lites of Mars, 336 ; satellites of Ju- 
piter, 350 ; satellites of Saturn, 362 ; 
satellites of Uranus, 363 ; satellite 
of Neptune, 368 ; of the connection 
between comets and meteors, 416; 
of spectroscopic binaries, 465**; of 
variable-star clusters, 455*. 
Dyne, value of, 97. 

E. 

Evolution of binary systems, 486, 466* 
note. 

F. 

Fifth satellite of Jupiter, 350. 

G. 

Gravitation, Constant of, 101. 

H. 

Hale, Prof. G. W., photography of 
solar prominences, 203. 

Helium, identification of, 202*; in 
meteorites, 401 ; in stars. 

Holmes' comet, 386, 399*. 

Huggins, Dr. W., attempt to photo- 
graph the corona without an eclipse, 
225*. 

Hussey, W. J., photograph of Ror- 
dame's comet, 399**. 

K. 

Keeler, J. E., spectroscopic observa- 
tion of Saturn's ring, 361 ; spectro- 
scopic motion of nebulae, 473. 



464 



SUPPLEMENTARY INDEX. 



[All references, unless expressly stated to the contrary, are to articles, not to pages.] 



Latitude of sun spots, Spoerer's law, 
190* ; variation of latitude, 71*. 

Lockyer, J. N., spectroscopic bina- 
ries, 465*. 

Lowell, P., observations of Mars, 333, 
333*, 336 ; of Mercury, 319 ; of Venus, 
323, 325. 

M. 

Megadyne, value of, 97. 

N. 

Nebulae, spectroscopic motion of, 473. 
Nova Aurigae and other "novae," 450. 

O. 

Oblate spheroid, mean diameter of, 95. 
Oppolzer, E., theory of sun spots, 
191. 



Parabolic velocity, the, 507*. 

Photographs of comets, 399**; of 
spectrum of the reversing layer, 198 ; 
of solar prominences, 203. 

Photography in the discovery of aste- 
roids, 338. 

Pickering, Prof. E. C, spectroscopic 
binaries, 465*. 

Pole, terrestrial, its motion, 71*. 

R. 

Reversing layer, Shackleton's photo- 
graph of its spectrum, 198. 

Richarz, determination of the den- 
sity of the earth, 108. 

Rordame's comet, photograph, 399**. 



S. 

Saturn's rings, spectroscopic observa- 
tion of, 361. 

Schaeberle, J. M., theory of the 
corona, 255*. 

Schiaparelli, Prof. G. V., on rota- 
tion of Mercury, 319 ; of Venus, 325. 

See, Prof. T. J., evolution of binary 
systems, 466* and 486, note ; orbits 
of binary stars, Appendix, Table VII. 

Shackleton, W., photograph of the 
spectrum of the reversing layer, 198. 

Sirius, orbit of, 464. 

Spectroheliograph, the, 203. 

Spoerer, G., law of sun-spot latitude, 
190*. 

T. 

Telluric lines in solar spectrum, 195. 



j Variable-star clusters, 455*. 

Variable stars discovered by photog- 
raphy, 455*. 

Variation of latitude (terrestrial), 
71*. 

Velocity, " parabolic" or critical, 
507*. 

Vogel, H. C, system of Algol, 454*; 
other spectroscopic binaries, 465*. 

W. 

Wolf, Max, photographic discovery 
of asteroids, 338. 



Yerkes telescope. 



URANOGRAPHY 



UKANOGKAPHY 



A BRIEF DESCRIPTION OF 



THE CONSTELLATIONS VISIBLE IN THE 
UNITED STATES 



WITH 

STAR-MAPS, AND LISTS OF OBJECTS OBSERVABLE 
WITH A SMALL TELESCOPE 



BY 

C. A3 YOUNG, Ph.D., LL.D. 

Professor of Astronomy in the College of New Jersey (Princeton). 



A SUPPLEMENT TO THE AUTHOR'S "ELEMENTS OF ASTRONOM1 
FOR HIGH SCHOOLS AND ACADEMIES" 



Boston, U.S.A., and London 



GINN & COMPANY, PUBLISHEBS 

1897 



Eotered at Stationers' Hall 



Copyright, 1889 and 1897, 
By CHARLES A. YOUNG. 



Atx Rights Reserved. 









PREFACE. 



This brief description of the constellations was pre- 
pared, at the suggestion of a number of teachers, as an 
integral part of the author's "Elements of Astronomy."" 
It has been thought best, however, for various reasons, 
to put it into such a form that it can be issued separately, 
and used if desired in connection with the larger " Gen- 
eral Astronomy," or with any other text-book. Since the 
Uranography also has to be used more or less in the open 
air at night, many will probably prefer to have it by itself, 
so that its use need not involve such an exposure of the 
rest of the text-book. All references marked Astr. are 
to the articles of the " Elements of Astronomy." 






ALPHABETICAL LIST OF THE CONSTELLATIONS DE- 
SCRIBED OR MENTIONED IN THE URANOGRAPHY. 



Andromeda 


Article 
16 


Anser, see Vulpeciila . 


54 


Antinous, see Aquila . 


56 


Antlia 


45 


Aquarius . 


63 


Aquila 


56 


Argo Navis 


34 


Aries 


19 


Auriga 


22 


Bootes 


42 


Camelopardus . 


14 


Cancer . 


35 


Canes Venatici . 


41 


Canis Major 


33 


Canis Minor 


31 


Capricornus 


58 


Cassiopeia 


9, 10 


Centaurus 


45 


Cepheus 


11 


Cetus . 


20 


Coma Beremcis 


40 


Columba . 


28 


Corona Borealis 


43 


Corvus 


38 


Crater . 


38 


Cygnus . 


53 


Delphinus . 


59 


Draco . 


12, 13 


Equiileus . 


60 


Eridanus . 


26 


Gemini . 


30 


Grus . 


64 


Hercules . 


50, 51 



Hydra 

Lacerta 

Leo . 

Leo Minor 

Lepus 

Libra 

Lupus 

Lynx 

Lyra 

Monoccraj 

Norma 

Ophiuchus 

Orion 

Pegasus 

Perseus 

Phoenix 

Pisces 

Piscis Australis 

(Pleiades) 

Sagitta 

Sagittarius 

Scorpio 

Sculptor . 

Serpens 

Serpentarius, see 

Sextans 

Taurus 

Taurus Poniatovii 

Triangulum 

Ursa Major 

Ursa Minor 

Virgo 

Vulpeciila . 



Article 
38 
61 
36 
37 
27 
44 
45 
29 
52 
32 
47 

48, 49 

24, 25 
62 
21 
20 
17 
64 
23 
55 
57 

46,47 
20 

48,49 
Ophiuchus 48, 49 



37 
23 

48 
18 
5-7 
8 
39 
54 



471 



UEANOGKAPHY. 



THE GTBEEK ALPHABET. 



Letters. 


Name. 


Letters. 


Name. 


Letters. 


Name. 


A, a, 


Alpha. 


i, i, 


Iota. 


P> P, V* 


Kho. 


B,j8, 


Beta. 


K, K, 


Kappa. 


2, (T, S 


, Sigma. 


r, 7, 


Gamma. 


A, A, 


Lambda. 


T,r, 


Tau. 


A, 8, 


Delta. 


M, fi, 


Mu. 


Y, v , 


Upsilon 


E, £ , 


Epsilon. 


N, v, 


Nu. 


<m, 


Phi. 


z, i 


Zeta. 


B,£ 


Xi. 


x > x> 


Chi. 


H > ty 


Eta. 


0,o, 


Omicron. 


*,& 


Psi. 


®, 0, * 


, Theta. 


n,^, 


Pi. 


O, 0), 


Omega. 



472 



UKANOGRAPHY, 



A Description of the Constellations. 

1. A general knowledge of the constellations sufficient to 
enable one to recognize readily the more conspicuous stars and 
their principal configurations, is a very desirable accomplish- 
ment, and not difficult to attain. It requires of course the 
actual study of the sky for a number of evenings in different 
parts of the year; and the study of the sky itself must be 
supplemented by continual reference to a celestial globe or 
star-map, in order to identify the stars observed and fix their 
designations. A well-made globe of sufficient size is the best 
possible help, because it represents things wholly without dis- 
tortion, and is easily " rectified " (Astr. 528 x ) for any given 
hour, so that the stars will all be found in the proper quarter 
of the (artificial) heavens, and in their true relations. But a 
globe is clumsy, inconvenient out of doors, and liable to dam- 
age; and a good star-map properly used will be found but 
little inferior in efficiency, and much more manageable. 

2. Star-Maps. — Such maps are made on various systems, 
each presenting its own advantages. None are without more 
or less distortion, especially near the margin, though they 
differ greatly in this respect. In all of them the heavens are 
represented as seen from the inside, and not as on the globe, 

1 The references are to the articles in the Author's " Elements of Astron- 
omy," to which this Uranography is a supplement. 

478 



8 URANOGRAPHY. [§ 2 

which represents the sky as if seen from the outside; i.e., the 
top of the map is north, and the east is at the left hand ; so 
that if the observer faces the south and holds up the map 
before and above him, the constellations which are near the 
meridian will be pretty truly represented. 

3. We give a series of four small maps which, though hardly on a 
large enough scale to answer as a satisfactory celestial atlas, are quite 
sufficient to enable the student to trace out the constellations and 
identify the principal stars. 

In the map of the north circumpolar regions (Map I.), the pole is 
in the centre, and at the circumference the right-ascension hours 
are numbered in the same direction as the figures upon a watch 
face; but with 24 hours instead of 12. The parallels of declination 
are represented by equidistant and concentric circles. On the three 
other rectangular maps, which show the equatorial belt of the heavens 
lying between + 50° and —50° of declination, the parallels of declina- 
tion are equidistant horizontal lines, while the hour-circles are vertical 
lines also equidistant, but spaced at a distance which is correct for 
declination 35°, and not at the equator. This keeps the distortion 
within reasonable bounds even near the margin of the map, and 
makes it very easy to lay off the place of any object for which the 
right ascension and declination are given. 

The hours of right ascension are indicated on the central hori- 
zontal line, which is the equator, and at the top of the map are given 
the names of the months. The iron! September, for instance, means 
that the stars which are directly under it upon the map will be near the 
meridian about nine o'cloclv in the evening during that month. 

4. The maps show all the stars down to the 4 £ magnitude — all 
that are easily visible on a moonlight night. A few smaller stars are 
also inserted, where they mark some peculiar configuration or point 
out some interesting telescopic object. So far as practicable, i.e., north 
of —30° Declination, the magnitudes of Pickering's "Harvard Pho- 
tometry " are used. The places of the stars are for 1900. 

Such double stars as can be observed with a three or four inch 
telescope are marked on the map by underscoring : two underscoring 
lines denote a triple star, and three a multiple. A variable star is 

474 



§ 4] THE CIRCUMPOLAR CONSTELLATIONS. 9 

denoted by a circle enclosing the star symbol. In the designation of 
clusters and nebulae the letter M. stands for " Messier," who made the 
first catalogue of 103 such objects in 1784; e.g., 97 M. designates No. 
97 on that list. A few objects from Herschel's catalogue are denoted 
by J$ with a number following. 

The student or teacher who possesses a telescope is strongly urged 
to get Webb's " Celestial Objects for Common Telescopes." It is 
an invaluable accessory. (Longmans, Green & Co., N. Y.) 

THE CIRCUMPOLAR CONSTELLATIONS. 

We begin our study of Uranography with the constellations 
which are circumpolar (i.e., within 40° of the north pole), 
because these are always visible in the United States, and so 
can be depended on to furnish land (or rather sky) -marks to 
aid in identifying and tracing out the others. 

5. Ursa Major, the Great Bear (Map I.). — Of these cir- 
cumpolar constellations none is more easily recognizable than 
Ursa Major. Assuming the time of observation as about eight 
o'clock in the evening on Sept. 22d (i.e., 20 h sidereal time), 
it will be found below the pole and to the west. Hold the 
map so that the VIII. is at the bottom, and it will be rightly 
placed for the time assumed. 

The familiar Dipper is sloping downward in the northwest, 
composed of seven stars, all of about the second magnitude ex- 
cepting 8 (at the junction of the handle to the bowl), which is 
of the third. The stars a and ji are known as the " Pointers," 
because the line drawn from (3 through a, and produced about 
30°, passes very near the Pole-star. 

The dimensions of the Dipper furnish a convenient scale of 
angular measure. From a to ft is 5° ; a to 8 is 10° ; (3 to y, 8° ; 
from a to rj at the extremity of the Dipper-handle (which is also 
the Bear's tail) is 26°. 

6. The Dipper (known also in England as the " Plough," 
and as the " Wain," or wagon) comprises but a small part of 

475 



10 URANOGRAPHY. T§ 6 

the whole constellation. The head of the Bear, indicated by 
a scattered group of small stars, is nearly on the line from S 
through a, carried on about 15° ; at the time assumed (20 h sid. 
time), it is almost exactly below the pole. Three of the four 
paws are marked each by a pair of third or fourth magnitude 
stars 1\° or 2° apart. The three pairs are nearly equidistant, 
about 20° apart, and almost on a straight line parallel to the 
diagonal of the Dipper-bowl from a to y, but some 20° south of 
it. Just now (20 h sid. time) they are all three very near the 
horizon for an observer in latitude 40°, but during the spring 
and summer they can be easily made out. 

7. Names 1 of Principal Stars. — 

€. Alioth. 

£. Mizar. The little star near it is 
Alcor, the "rider on his horse." 
rj. Benetnasch or Alkaid. 

Double Stars: (1) £ (Mizar), Mags. 3 and 5; Pos. 2 149°; Dist. 
14".5. In looking at this object the tyro will be apt to think that the 
small star shown by the telescope is identical with Alcor : a very low 
power eye-piece will correct the error. (Astr. Fig. 113.) The large 
star is itself a " spectroscopic binary" (see Art. 465*). (2) £, th^ 
southern one of the pair which marks the left hind paw. Binary: 
Mags. 4 and 5; Pos. (1890) (about) 220°, Dist. (about) 2". Position 
and distance both change rapidly, the period being only 61 years. 
This was the first binary whose orbit was computed. 

Clusters and Nebuhe: (1) 81 and 82 M., A.R. 9 h 45™, Dec. 69° 44'. 
Two nebulae, one pretty bright, about half a degree apart. (2) 97 M., 
A.R. ll h 07 m , Dec. 55° 43'— 2° south-following /J. A planetary nebula. 



a. 


JJUBHE. 


fi. 


Merak. 


r- 


Phecda. 


8. 


Megrez. 



1 Capitals denote names that are generally used ; the others are met with 
only rarely. 

2 The " position angle" of a douhle star is the angle which the line drawn 
from the larger star to the smaller one makes with the hour-circle. It is 
always reckoned from the north completely around through the east, as 
shown in Fig. A. 

476 



IS] 



URSA MINOR, THE LESSER BEAR. 



11 



8. Ursa Minor, the Lesser Bear (Map I.). — The line of the 
"Pointers" unmistakably marks out the Pole-star ("Polaris" 
or "Cynosura"), a star of the second magnitude standing alone. 
It is at the end of the tail of Ursa Minor, or at the extremity 
of the handle of the "Little Dipper," for in Ursa Minor, also, 
the seven principal stars form a dipper, though with the handle 
bent in a different 

way from that of 
the other Dipper. 
Beginning at "Po- 
laris " a curved line 
(concave towards 
Ursa Major) drawn 
through 8 and e 
brings us to £, where 
the handle joins the 
bowl. Two bright 
stars (second and 
third magnitude), /? 
and y, correspond to 
the pointers in the 
larger Dipper, and 
are known as the 
"Guardians of the 
Pole": /? is called 

"KochabP The remaining corner cf the bowl is marked by 
the faint star rj with another still smaller one near it. 

The Pole lies about 1^° from the Pole-star, on the line joining 
it to £ Ursse Majoris (at the bend in the handle of the large 
Dipper). 

Telescopic Object. Polaris has a companion of the 9 J magnitude, 
distant 18". 6, — visible with a two-inch telescope. 

9. Cassiopeia (Map I.). — This constellation lies on the 
opposite side of the pole from the Dipper at about the same 

477 




Fig. A. — Measurement of Distance and Position- Angle 
of a Double Star. 



12 URANOGRAPHY. [§ 9 

distance as the "Pointers," and is easily recognized by the 
zigzag, " rail-fence " configuration of the five or six bright stars 
that mark it. With the help of the rather inconspicuous star 
k, one can make out of them a pretty good chair with the feet 
turned away from the pole. But this is wrong. In the recog- 
nized figures of the constellation the lady sits with feet towards 
the pole, and the bright star a is in her bosom, while £ and the 
other faint stars south of a, are in her head and uplifted arms : 
i, on the line from S to c produced, is in the foot. The order 
of the principal stars is easily remembered by the word Bagdei; 

i.e., (3, a, y, 8, e, i. 

Names of Stars : a (which is slightly variable) is known as Schedir ; 
/? is called Caph. 

Double Stars: (1) rj, Mags. 4-7J. Large star orange; small one 
purple. Pos. 170° ±, Dist. 5". 5. Binary, with a period of some 200 
years. Easily recognized by its position about half-way between a 
and y, a little off the line. (2) if/, A.R. l h 17 m , Dec. 67° 21' ; Triple ; 
Mags. 4J, 9 and 9 ; Pos. A to (B + C) 106°, Dist. 29"; Pos. B-C 257°, 
Dist. 2". 9. Found on a line from rj through y produced three times 
the distance rj-y: rather difficult for a four-inch telescope. 

10. The Sidereal Time determined by the Apparent Position 
of Cassiopeia. — The line from the Pole-star through Caph or (3 
Cassiopeia? (which is the leader of all the bright stars of the constella- 
tion in their daily motion) is almost exactly parallel to the Equinoc- 
tial Colure. When, therefore, this star is vertically above the Pole-star 
it is sidereal noon ; it is 6 h when it is on the great circle (not the par- 
allel of altitude) drawn from the Pole-star to the west point of the 
Horizon ; 12 h when vertically below it ; and 18 h when due east. A 
little practice will enable one to read the sidereal time from this celes- 
tial clock with an error not exceeding 15 or 20 minutes. 

11. Cepheus (Map I.). — This constellation contains very 
few bright stars. At the assumed time (20 h sidereal) it is 
above and west of Cassiopeia, not having quite reached the 
meridian above the pole. A line carried from a Cassiopeise 
through /?, and produced 20° (distance a . . . /? = 5° nearly) 

478 



§ 11] DRACO. 13 

will pass very near to a Cephei, a star of the third magnitude, 
in the king's right shoulder. j3 Cephei is about 8° due north of 
a, and y about 12° from /?, both also of third magnitude : y is so 
placed that it is at the obtuse angle of a rather flat isosceles 
triangle of which (3 Cephei and the Pole-star form the two other 
corners. Cepheus is represented as sitting behind Cassiopeia 
(his wife) with his feet upon the tail of the Little Bear, y being 
in his left knee. His head is marked by a little triangle of 
fourth magnitude stars, 8, e, and £, of which 8 is a remarkable 
variable with a period of 5±- days (see Astr. Table IV.). 
There are several other small variables in the same neighbor- 
hood, but none of them are shown on the map. 

Names of Stars: a is Alderamin, and /3 is Alphirk. 

Double Stars: (1) (3, Mags. 3 and 8; Pos. 251°; Dist. 14". (2) 8, 
Mags, larger star 3.7 to 5 (variable), smaller one 7; Pos. 192°, Dist. 
41" ; Colors, yellow and blue. (3) k, A.R. 20 h 13 m , Dec. 77° 19' ; Mags. 
4.5 and 8.5; Pos. 124°; Dist. 7."5; Colors, yellow and blue. 

12. Draco (Map I.). — The constellation of Draco is char- 
acterized by a long, sinuous line of stars, mostly small, extend- 
ing half-way around the pole and separating the two Bears. 
A line from 8 Cassiopeise drawn through /? Cephei and ex- 
tended about as far again will fall upon the head of Draco, 
marked by an irregular quadrilateral of stars, two of which 
are of the 2\ and 3d magnitude. These two bright stars about 
4° apart are /? and y ; the latter in its daily revolution passes 
almost exactly through the zenith of Greenwich, and it was by 
observations upon it that the aberration of light was discovered 
(Astr. 125). The nose of Draco is marked by a smaller star, n, 
some 5° beyond /3, nearly on the line drawn through it from y. 
From y we trace the neck of Draco, eastward and downward * 
towards the Pole-star until we come to 8 and e and some smaller 
stars near them. There the direction of the line is reversed, 






1 The description here applies strictly only at 20 h sid. time. 

479 



14 TJKANOGRAPHY. [§ 12 

so that the body of the monster lies between its own head and 
the bowl of the Little Dipper, and winds around this bowl until 
the tip of the creature's tail is reached at the middle of the 
line between the Pointers and the Pole-star. The constella- 
tion covers more than 12 h of right ascension. 
/ 

13. One star deserves special notice : a, a star of the 3\ 

magnitude which lies half-way between Mizar (£ Urs. Maj.) 
and the Guards (/? and y Urs. Min.) ; 4700 years ago it was 
the Pole-star, within 10 f or 15' of the pole, and much nearer 
than Polaris is at present, or ever will be. It is probable 
that its brightness has considerably diminished within the 
last 200 years ; since among the ancient and mediaeval astron- 
omers it was always reckoned of the second magnitude. 

Names of Stars : a is Thubax ; ft, Alwaid ; and y, Etanin. 

Double Stars: (1) jjl, Mags. 4 and 4|; Pos. 165°; Dist. 2".5. Bi- 
nary, with a probable period of about 600 years. (2) c, Mags. 4, 
8; Pos. 0°.0; Dist. 2".9 ; yellow and blue. Nebula, A.R. 17 h 59 m ; 
Dec. 66° 38 . Planetary, like a star out of focus. This object is 
almost exactly at the pole of the ecliptic, about midway between 8 and 
£ Draconis, but a little nearer £. 

14. CamelopardllS (Map L). — This is the only remaining one 
of the strictly circumpolar constellations — a modern asterism contain- 
ing no stars above fourth magnitude, and constituted by Hevelius 
simply to cover the great empty space between Cassiopeia and Perseus 
on one side, and Ursa Major and Draco on the other. The animal 
stands on the head and shoulders of Auriga, and his head is between 
the Pole-star and the tip of the tail of Draco. 

The two constellations of Perseus (which at 20 h sidereal time is 
some 20° below Cassiopeia) and of Auriga are partly circumpolar, but 
on the whole can be more conveniently treated in connection with the 
equatorial maps. Capella, the brightest star of Auriga, and next to 
Vega and Arcturus the brightest star in the northern hemisphere, at 
the time assumed (Sept. 22, 8 p.m.), is a few degrees above the horizon 
in the N.E. Between it and the nose of Ursa Major is part of the 
constellation of the Lynx, — a modern asterism made, like Camelopar- 
dus, merely to fill a gap. 

480 



§ 15] MILKY WAY IN CIRCUMPOLAR REGION. 15 

15. The Milky Way in the Circumpolar Region. — The only 
circumpolar constellations traversed by it are Cassiopeia and 
Cepheus. It enters the circumpolar region from the constella- 
tion of Cygnus, which at 20 h sidereal time is just in the zenith, 
sweeps down across the head and shoulders of Cepheus, and 
on through Cassiopeia and Perseus to the northeastern horizon 
in Auriga. There is one very bright patch a degree or two 
north of j3 Cassiopeise ; and half-way between Cassiopeia and 
Perseus there is another bright cloud in which is the famous 
cluster of the "Sword Handle of Perseus " — a beautiful object 
for even the smallest telescope. 



16. Andromeda (Map II.). — Passing now to the equato- 
rial maps and beginning with the northwestern corner of Map 
No. II., we come first to the constellation of Andromeda, which 
will be found exactly overhead in our latitudes about 10 o'clock 
in the middle of November, or at 8 o'clock a month later. Its 
characteristic configuration is the line of three second-magni- 
tude stars, a, /?, and y, extending east and north from a, which 
itself forms the N".E. corner of the so-called " Great Square of 
Pegasus," and is sometimes lettered as 8 Pegasi. This star 
may readily be found by extending an imaginary line from 
Polaris through /? Cassiopeise, and producing it about as far 
again : a is in the head of Andromeda, /? in her waist, and y 
in the left foot. About half-way from a to /?, a little south 
of the line, is 8 (of the third magnitude) with ?r and € of the 
fourth magnitude near it. A line drawn northwesterly from 
f3 nearly at right angles to the line )3y, will pass through /x at 
a distance of about 5°, and produced another 5° will strike 
the "great nebula" (Astr. 470), which forms a little obtuse- 
angled triangle with v and a sixth-magnitude star known as 
32 Andromedse. 

Andromeda has her mother, Cassiopeia, close by on the north, and 
at her feet is Perseus, her deliverer, while her head rests upon the 

481 



16 CJRANOGRAPHY. L8 l,; 

shoulder of PegaSUS, the Winged horse which 1 >ioul;1iI Persens to her 

rescue. To the south, beyond the intervening constellations of Aries 
and Pisces, Cetus, the sea-monster, who was to have devoured her, 
s( retches his ungainly hulk. 

Names of Stars, a, Alpheratz; /?, Mirach} y, Almaach, 

/)<>,<!>/<■ Stars. (1) y, MftgS. 3, 5; POS, 62°j Dist, 11"; colors, 

orange and greenish blue a beautiful object. The small star is 
itself double, bu1 at present so close as fco be beyond the reach of any 
hui very large instruments (Astr, Pig. L13). (2) w (2° X. and a 
little wdst of 8), Mags. 4, 9; Pos, 174°; Dist. 86"; white and blue. 

Nebulas. M. 31 j the great nebula; visible to naked eye. M,32; 
small, round, and bright, is in the same low-power field with 81| 

S0U.1 h and east oi' it. 

17. Pisces (Map LI.). — Immediately south o\' Auadromeda 

lies Pisces, the first of the zodiaeal const el hit ions, though now 

occupying (in consequence of preoession) the sign of Aries. 
It has not. a single conspicuous star, and is notable only as con- 
taining the vernal equinox, or first of Aries, which lies near 
the southern boundary o( the constellation in a peculiarly star- 
less region. A line from a A-ndromedse through y Pegasi con- 
tinued as far again strikes about. 2° oast o\' the equinox, 

The body of the southern tish lies about 15° south of the middle of 

the southern side o( the great square o( Pegasus, ami is marked by an 
irregular polygon o^i small stars, 5° or 6° in diameter, A long crooked 

-• ribbon " oi little stars inns eastward for more than 80°, terminating 
in u risciuni, called El Ixisclia, a star o\' the fourth magnitude 20° 
south o[ the head oi Aries. from there another line of stars leads up 
\AY. in the direction o( <S Andromeda 4 io the northern tish, which lies 
in the vacant, space south o( f} Andronied;e. 

Double Stars. ( l) <*, Mags, I, 5.6 j Pos, 824° j Dist. 8", (i?) 
i//' (2° s.K. o\' >) Andromeda* -see map), Mags. 4,9, 5 j Vo*. L60°j 
Dirt. ;;i". 

18. Triangulum (Map [I.). — This little constellation, insignifl? 

cant as it is, is one o( Ptolemy's ancient IS. It lies halfway be- 
tween y Andromeda 4 and the head o( Aries, characterized by three 
stars oi the third ami fourth magnitudes, 

-1SJ 



$ 1«J ' AKIKS. 17 

Double Stars. (1) i or 6 (5° nearly due south of ft Trianguli, and 
at the obtuse angle of an isosceles triangle of which «, and y are the 
other two corners), Mags. 5, 6.5; Pos. 76°; Dist. 1"; topaz-yellow 
and green. 

19. Aries (Map II.)- — This is the* second of the zodiacal 
constellations (now occupying the sign of Taurus). It Is bounded 
north by Triangulum and Perseus, west by Pisces, south by 
Cetus, and east by Taurus. The characteristic star-group is 
that composed of a, /?, y (see map), about 20° due south of y 
Andromedae: a, a star of the 2\ magnitude is fairly conspicu- 
ous, forming as it does a large isosceles triangle with ft and y 
Andromedae. 

Names oj' Stars, a, llamil ; ft, Slwratan; y, Mfsartim. 

Double Stars. (1 ) y, Mags. 4.5, 5 ; Pos. 0°; Dist. 8".8. (This is 
probably the earliest known double star; noticed by Uooke in 1664.) 
(2) c, Mags. 5, 6.5; Pos. 200°; Dist. L".2. (About one-third of the 
way from a Arietis towards Aldebaran, £ is T J beyond it on the same 
line.) Tins is probably too difficult for any instrument less than 4 or 
1 ; , inches' aperture. ( ; >j ir, Triple; Mags. 5, 8.5, and 11; A-B, Pos. 

122° j Dist. 3".] ; A-C, Pos. 110° J Dist. 25". (At the southern coiner 
of a nearly isosceles triangle formed with c and £, e being at the ohtuse 
angle.) 

The star 41 Arietis (8J mag.), whidi forms a nearly equilateral tri- 
angle with a Arietis and y Trianguli, constitutes, with two or three 
other small stars near it, the constellation of Musca (Boreal is), a con- 
stellation, however, not now generally recognized. 

20. Cetus (Map II.). — South of Aries and I'iseos lies the 
huge constellation of Cetus, which backs up Into tin; sky from 
the southeastern horizon. The head lies some 20° S.K. of a 
Arietis, marked by an Irregular pentagon of stars, each side of 

which is 5° or 6° long. The southern edge of it is formed by 
the stars a (2} z mag.) and y (.'>*, mag.) : o lies nearly south of 
y. ft, the brightest star of the constellation (2d magnitude), 

stands alone nearly '10° west and south of a. About half-way 

led 



18 URANOGRAPHY. [§20 

from /? to y the line joining them passes through a character- 
istic quadrilateral (see map), the N.E. corner of which is com- 
posed of two fourth-magnitude stars, £ and ^. The remarkable 
variable o Ceti (Mira) lies almost exactly on the line joining 
y and £, a little nearer to y than to £. It is visible to the naked 
eye for about a month or six weeks every eleven months, 
when near its maximum. 

Names of Stars, a, Menkar ; (3, Diphda or Deneb Kaitos ; £, Baten 
Kaitos ; o, Mira. 

Double Stars. (1) y, Mags. 3.5,7; Pos. 290°; Dist. 2".5; yellow 
and blue. 

South of Cetus lies the constellation of Sculptoris Apparatus (usu- 
ally known simply as Sculptor), which, however, contains nothing 
that requires notice here. South of Sculptor, and close to the horizon, 
even when on the meridian, is Phoenix. It has some bright stars, 
but none easily observable in the United States. 

21. Perseus (Maps I. and II.). — Eeturning now to the 
northern limit of the map, we come to the constellation of 
Perseus. Its principal star is a, rather brighter than the 
standard second magnitude, situated very nearly on the pro- 
longation of the line of the three chief stars of Andromeda. 
A very characteristic configuration is "the segment of Per- 
seus" (Map I.), a curved line, formed by 8, a, y, and rj, with 
some smaller stars, concave towards the northeast, and run- 
ning along the line of the Milky Way towards Cassiopeia. 
The remarkable variable star /?, or Algol (Astr. 453), is situ- 
ated about 9° south and a little west of a, at the right angle 
of a right-angled triangle which it forms with a (Persei) and 
y Andromedae. Some 8° south and slightly east of 8 is e, and 
8° south of € are £ and o of the fourth magnitude in the foot of 
the hero. Algol and a few small stars near it form " Medusa's 
Head." 

Names of Stars, a is Marfak, or Algenib; f3 is Algol. 
Double Stars. (1) e, Mags. 3.5, 9; Pos. 10°; Dist. 8".4. (2) £ 

484 









§ 21] AURIGA. 19 

Quadruple; Mags. 3.5, 10, 11, 12; Pos. A-B, 207°; Dist. 13".2, 83", 
121". (3) rj, Mags. 5, 8.5; Pos. 300°; Dist. 28"; orange and blue. 

Clusters. (1) # VI. 33 and 34. Magnificent. Half-way between 
y Persei and 8 Cassiopeise. (2) M. 34; A.R. 2 h 34'"; Dec. 42° 11'; 
coarse, w r ith a pretty double star (eighth mag.) included. 

22. Auriga (Maps I. and II.). — Proceeding east from. Per- 
seus we come to Auriga, instantly recognized by the bright 
yellow star Capella (the Goat) and her attendant Hcedi (or 
Kids). Capella, a Aurigse, according to Pickering, is precisely 
of the same brightness as Vega (Mag. = 0.2), both of them 
being about i of a magnitude fainter than Arcturus, but dis- 
tinctly brighter than any other stars visible in our latitudes 
except Sirius itself. About 10° east of Capella is ft Aurigae 
of the second magnitude, and 8° south of ft is 6 of the third 
magnitude ; 8 Aurigae is 10° north of ft in the circumpolar 
region, e, £, and rj, 4° or 5° S.W. of a, are the "Kids." 

Names of Stars, a, Capella; ft, Menkalinan. 

Double Stars. (1) a>, Mags. 5, 9; Pos. 353°; Dist. 7"; white, light 
blue, ft is a spectroscopic double (see Art. 465*). 

Clusters. (1) M. 37; A.R. 5 h 44 m ; Dec. 32° 31' (on the line 
from Aurigse to £ Tauri, one-third of the w 7 ay from 6). Fine for 
small instrument. (2) M. 38; A.R. 5 h 21 m ; Dec. 35° 47'. Nearly 
at the middle of the line from 6 to w. (3) M. 36; A.R. 5 h 28 m ; Dec. 
34° 3'. One-third of the way from M. 38 to M. 37. 

23. Taurus (Map II.).— This, the third of the zodiacal 
constellations, is bounded north by Perseus and Auriga, west 
by Aries, south by Eridanus and Orion, and east by Orion and 
Gemini. It is unmistakably characterized by the Pleiades, 
and by the V-shaped group of the Hyades which forms the 
face of the bull, with the red Aldebaran (a Tauri) blazing in 
the creature's eye, as he charges down upon Orion. His horns 
reach out towards Gemini and Auriga, and are tipped with the 
second and third magnitude stars ft and £. As in the case of 
Pegasus, only the head and shoulders appear in the consteHa- 

485 



20 URANOGRAPHY. [§ 23 

tion. Six of the Pleiades are easily visible, and on a dark night 
a fairly good eye will count nine (see Astr. 469). With a 
3-inch telescope about 100 stars are visible in the cluster. In 
the Hyades the pretty naked-eye double 6 h 2 , is worth noting. 

Names of Stars, a, Aldebaran; /?, El Nath ; rj (the brightest of 
the Pleiades), Alcyone. For the names of the other Pleiades, see the 
figure in Art. 469 of the Astronomy. 

Double Stars. (1) a has a small, distant companion, 12th magni- 
tude; Pos. 36°; Dist. V 48". It has also a second companion much 
nearer and more minute, but far beyond the reach of ordinary tele- 
scopes. (2) r, Mags. 5 and 8 ; Pos. 210° ; Dist. 62 ' ; white and violet. 
Found by drawing a line from y (at the point of the V of the Hyades) 
through e, and producing it as far again (accidentally omitted on the 
map) . 

Nebula. M. 1; A.R. 5 h 27 m ; Dec. 21° 56', about 1° west and a 
little north of £. Often mistaken for a comet. The so-called "Crab 
Nebula." 

24. Orion (not O'-ri-on) (Map II.). — On the whole this is 
the finest constellation in the heavens. As he stands facing 
the bull his shoulders are marked by the two bright stars, a 
and y, the former of which in color and brightness closely 
matches Aldebaran. In his left hand he holds up the lion 
skin, indicated by the curved line of little stars between y and 
the Hyades. The top of the club, which he brandishes in his 
right hand, lies between £ Tauri and /x and rj Geminorum. His 
head is marked by a little triangle of stars of which A is the 
chief. His belt consists of three stars of the second magni- 
tude pointing obliquely downward towards Sirius. It is very 
nearly 3° in length, with the stars in it equidistant like a 
measuring-rod, so that it is known in England as the "Ell 
and Yard." From the belt hangs the sword, composed of three 
smaller stars lying more nearly north and south : the middle 
one of them is the multiple 6 in the great nebula. /? Orionis, 
or Rjgel, a magnificent white star, is in the left foot, and k is 
in the right knee. Orion has no right foot, or if he has, it is 

486 



§ 24 ] ERIDANL\S. 21 

hidden behind Lepus. The quadrilateral a, y, &, k, with the 
diagonal belt 8, e, £, once learned can never be mistaken for 
anything else in the heavens. 

25. Names of Stars, a, Betelgeuse; (3, Rigel; y, Bellatrix; 
k, Saiph; S. Mintaka; e, Alnilam; £, Alnitak. 

Double Stars. In these Orion is remarkably rich. (1) [3 (Rigel), 
Mags. 1 and 9; Pos. 200°; Disk. 9". 5; both white, — a beautiful and 
easy object. (2) 8 (the westernmost star in the belt), Mags. 2.5 and 
7: Pos. 0; Disk 53". (3) £, Triple; Mags. 2.5, 6.5, 10; A-B, Pos. 
155°, Dist. 2".4: A-C, Pos. <J' : , Disk 59". (4) t. Triple; Mags. 3.5, 8.5, 
11 ; A-B, Pos. 142°, Dist. 11".5; A-C, Pos. 103°, Dist. 49". (This is 
the lowest star in the sword, just below the nebula.) (5) 0, Multiple, 
the trapezium in the nebula. Four stars are easily seen by small 
telescopes (Astr. Fig. 113). (0) o-, Triple: Mags. 4,"s, 7 ; A-B, Pos. 
84°, Dist. 12".5; A-C, Pos. 61°, Dist. 42" (l, c S.W. of £). 

Nebula. M. 42 ; attached to the multiple star 0. The nebula of all 
the heavens ; by far the finest known, though in a small telescope 
wanting much of the beauty brought out by a larger one. 

26. EridSnus (Map II.). — This constellation lies south of 
Taurus, in the space between Cetus and Orion, and extends far 
below the southern horizon. Its brightest star a (Achekxak) 
is never visible in the United States. 

Starting with f3 of the third magnitude, about 3° north and 
a little west of Rigel (J3 Orionis) ; one can follow a sinuous line 
of stars, some of them of the third and fourth magnitudes, 
westward about 30° to the paws of Cetus, 10° south of a Ceti ; 
there the stream turns at right angles southwards for 10°, then 
southeast for about 20°, and finally south westward to the hori- 
zon. One could succeed in fully tracing it out, however, only 
by help of a map on a larger scale than the one we are able 
to present. 

Names of Star.-. [3. Cursa : y, Zaurach 

Double Stars. (1) 32; A.R. 3" 48'", Dec. S. 3° 19'; Mags, o, 7; 
Pos. 347°; Dist. 6".6; yellow, blue; very fine. (2) o 2 , Triple: A.R 

4*7 



22 URANOGRAPHY. [§ 26 

4 h 10 m ; Dec. S. 7° 50'; Mags. 5, 10, 10; Pos. A, ( B + C) , 108°; Dist. 
83" ; Pos. B-C, 110°, Dist. 4" ; very pretty. 

27. Lepus (Map II.). — This little constellation (one of the 
ancient 48) lies just south of Orion, occupying a space of some 15° 
square. Its characteristic configuration is a quadrilateral of third 
and fourth magnitude stars, with sides from 3° to 5° long, 10° south 
of k Orionis, and 15° west and a little south of Sirius. 

Double Stars. (1) y (the S.E. corner of the quadrilateral) is a 
coarse double. Mags. 4, 6.5 ; Pos. 350° ; Dist. 93". (2) k (5J° south 
of Rigel), Mags. 5 and 9 ; Pos. 0°; Dist. 3".7. 

28. Columba (Noah's Dove) (Map II.). — This is next south of 
Lepus : too far south to be well seen in the Xorthern States. Its prin- 
cipal star, q, or Phact, of the 2 J magnitude, is readily found by draw- 
ing a line from Procyon to Sirius, and prolonging it nearly the same 
distance. And in passing we may note that a similar line drawn from 
a Orionis through Sirius and produced, will strike near £ Argus, or 
" Naos" a star about as bright as Phact, — the two lines which inter- 
sect at Sirius making the so-called "Egyptian X." 

29. Lynx (Map I., II., and III.). — Returning now to the north- 
ern limit of the map, we find the modern constellation of the Lynx 
lying just east of Auriga and enveloping it on the north and in the 
circutnpolar region. It contains no stars above the fourth magnitude, 
and is of no importance except as occupying an otherwise vacant 
space. 

Double Stars. (1) 38, or p Lyncis, A.R. 9 h ll m ; Dec. 37° 21'"; Mags. 
4, 7.5; Pos. 240°; Dist. 2".9 ; white and lilac. (This is the northern 
one of a pair of stars which closely resembles the three pairs that 
mark the paws of Ursa Major. This pair makes -nearly an isosceles 
triangle with the two pairs A/x and i k, Ursae Majoris — see map.) 

30. Gemini (Map II.). — This is the fourth of the zodiacal 
constellations (mostly in the sign of Cancer), containing the 
summer solstitial point about 2° west and a little north of the 
star r). It lies northeast of Orion and southeast of Auriga, 
and is sufficiently characterized by the two stars a and /? (about 
4^-° apart), which mark the heads of the twins. The southern 

488 



§ 30] CANIS MINOR. 23 

one, (3, or Pollux, is the brighter, but a (Castor) is much the 
more interesting, as being double. The feet are marked by 
the third-magnitude stars y and /x, some 10° east of £ Tauri, 
and the map shows how the lines that join these to ft and a 
respectively mark the places of 8 and e. rj, 2° west of /x, is a 
variable, and is also double, though as such it is beyond the 
power of ordinary telescopes. 

Names, a, Castor ; /?, Pollux; y, Alhena ; //,, Tejat (Post); 
rj, Tejat (Prior) ; 8, Wasat; e, Meboula. 

Double Stars. (1) a, Mags. 2.5, 3; Pos. 225°; Dist. 5". 5. Binary; 
period undetermined, but certainly over 200 years. The larger of 
the close pair is also a spectroscopic binary, with period of about 3 
days (see Art. 465*). There is also a companion of ninth mag., dis- 
tant about 74"; Pos. 164°. (2) 8, Mags. 3, 8 ; Pos. 203°; Dist, 7". 
(3) /*, Mags. 3, 11 ; Pos. 79°; Dist. SO". 

NebulcB and Clusters. (1) M. 35; A.R. h 01-; Dec. 21° 21'; X.W. 
of 7) at the same distance as that from jul to rj, and on the line from y 
through rj produced. The map is not quite right in this respect. 
(2) # IV. 45; A.R. 7 h 22'*; X, 21° 10'. A nebulous star in a small 
telescope : in a large telescope, very peculiar — 2° southeast of 8. 

31. Canis Minor (Map II.). — This constellation, just south 
of Gemini, is sufficiently characterized by the bright star 
Procyox, which is 25° due south of the mid-point between 
Castor and Pollux, a. /?, and y together form a configuration 
closely resembling that formed by a, (3, and y Arietis. Pro- 
cyon, a Orionis, and Sirius form nearly an equilateral triangle 
with sides of about 25°. 

Names, a, Procyox ; (3, Gomelza. 

Double Stars. (1) Procyon has a small companion, Dist. 40 ;/ , Pos. 
312°, — too small, however, for anything less than an 8-inch telescope. 
In 1896 a still smaller companion, like that of Sirius, was found 
much nearer the large star. (See Art. 461.) (2) (2 1126) (following 
Procyon 43 s , and 2' south, — the brightest of the stars in that field), 
Mags. 7, 7.5 ; Pos. 145°: Dist. 1".5 : a good test for a 4-inch ^]^$. 

489 



24 URANOGRAPHY. [§ 32 

32. Monoceros (The Unicorn) (Map I L). — This is one of the 
new constellations organized by Hevelius to fill the gap between Gem- 
ini and Canis Minor on the north, and Argo Navis and Canis Major 
on the south. It lies just east of Orion. It has no conspicuous stars, 
but is traversed by a brilliant portion of the Milky Way. The a 
(fourth mag.) of the constellation lies about half-way between a 
Orionis and Sirius, a little west of the line joining them. 

Double Stars. (1) 8, or b (7£° east and 3° south of a Orionis), 
Mags. 5, 8; Pos. 24°; Dist. 12".9 ; colors, orange and lilac. A fine 
low-power field. (2) 11 Monocerotis, a fine triple (see Fig. 113 of 
Astr.), A.R. 6 h 24 m ; Dec. south 6° 57'; A to B-C, Pos. 130°, Dist, 8" ; 
B-C, Pos. 120°, Dist. 2". 5. The star is very nearly pointed at by a 
line drawn from £ Canis Majoris, north through /3, and continued as 
far again. 

Clusters. (1) # VII. 2 ; A.R. 6 h 24 m ; Dec. N". 5° 2' (visible to the 
naked eye about 1^° N.E. of 8 Monocerotis described above). A fine 
cluster for a low power. (2) M. 50 ; A.R. 6 h 57 m ; Dec. S. 8° 9'. 
In the Milky Way, on the line from Sirius to Procyon, two-fifths of 
the distance. 

33. Canis Major (Map II.) . — This glorious constellation 
needs no description. Its a is the Dog Star, Sirius, beyond 
all comparison the brightest in the heavens, and probably one 
of our nearer neighbors. It is nearly pointed at by the line 
drawn through the three stars of Orion's belt. f3, at the ex- 
tremity of the uplifted paw, is of the second magnitude, and 
so are several of those farther squth in the rump and tail of 
the animal, who sits up watching his master Orion, but with 
an eye out for Lepus. 

Names, a, Sirius; (3, Mirzam; y, Muliphen ; 8, Wesen ; c, Adara. 
y is said to have disappeared from 1670 to 1690, but at present is not 
recognized as variable, though much fainter than would be expected 
from its being lettered as y. 

Double Stars. (1) Sirius itself has a small companion (see Art. 
■KM). (2) fi (4° N.E. of Sirius), Mags. 5, 9.5 ; Pos. 385°; Dist. 3".5. 

Clusters. (1) M. 41 (4° south of Sirius) ; a fine group with a red 
star near centre. 

490 



§ 34] AKGO NAVIS. 25 

34. Argo Navis (The Ship) (Maps II. and III.). — This is one 

of the largest, most important, and oldest of the constellations, lying 
south and east of Canis Major. Many Uranographers now divide it 
into three, Puppis, Vela, and Carina. Its brightest star, a Argus, 
Caxopus, ranks next to Sirius, but is not visible anywhere north of 
the parallel of 38°. The constellation, huge as it is, is only a half 
one, like Pegasus and Taurus, — only the stern of a vessel, with 
mast, sail, and oars ; the stem being wanting. In the part of the 
constellation covered by our maps the most conspicuous stars lie east 
and southeast of Canis Major. We have already mentioned f , or Naos 
(Art. 28), at the southeast extremity of the "Egyptian X"; and about 
8° south and a little east of it is y, nearly of the second magnitude. 

Clusters. One or two clusters are accessible in our latitudes. 
(1) (9 VIII. 38), A.R. 7 h 31 m ; Dec. S. 14° 12'. Pointed at by the line 
from /3 Can. Maj. through Sirius, continued 2\ times as far. Visible 
to naked eye; rather coarse. (2) M. 46; a little more than 1° east 
and south of the preceding. (3) M. 93, A.R. 7 h 39 m ; Dec. S. 23° 34'; 
about 2° N.W. of £ Argus. 

35. Cancer (Maps II. and III.). — This is the fifth of the 
zodiacal constellations, bounded north by Lynx and Leo Minor, 
south by the head of Hydra, west by Gemini and Canis Minor, 
and east by Leo. It does not contain a single conspicuous 
star, but is easily recognizable from its position, and in a dark 
night by the nebulous cloud known as "Prsesepe," or the 
" Manger," with the two stars y and 8 near it, — the so-called 
" Aselli," or " Donkeys." Prsesepe (sometimes also called the 
"Beehive") is really a coarse cluster of seventh and eighth 
magnitude stars, resolvable by an opera-glass. The line from 
Castor through Pollux, produced about 12°, passes near enough 
to it to serve as a pointer, a, of the fourth magnitude, is on 
the line drawn from Prsesepe through 8 (the southern Asellus), 
produced about 7° ; /3 may be recognized by drawing a line 
from y (the northern Asellus) through Prsesepe, and continu- 
ing it about 12°. 

Double Starrs. (1) i, Mags. 4, 6.5; Pos. 308°; Dist. 30 '; orange and 
blue ; nearly due north of y, distance twice that between the Aselli. 

491 



26 TJRANOGRAPHY. [§ 35 

(2) £, Triple (see Astr. Fig. 113); A-B, Mags. 6 and 7, Pos. (1890) 
350°, Dist. l' f ; in rapid motion ; period about 60 years. A-C, Pos. 
(1890) 125°, Dist. 5" ; also in motion, but period unknown and much 
longer. Easily found by a line from a Gem. through f3, produced two 
and a half times as far. 

36. Leo (Map III.). — East of Cancer lies the noble con- 
stellation of Leo, which adorns the evening sky in March and 
April ; it is the sixth of the zodiacal constellations, now occu- 
pying the sign of Virgo. Its leading star Kegulus, or " Cor 
Leonis" is of the first magnitude, and two others, (S and y, are 
of the second, a, y, S, and /? form a conspicuous irregular 
quadrilateral (see map), the line from Kegulus to Denebola 
being 26° long. Another characteristic configuration is "The 
Sickle," of which a, rj is the handle, and the curved line rj, y, £, 
fx, and e is the blade, the cutting edge being turned towards 
Cancer. The " radiant " of the November meteors lies between 
£ and e. 

Names, a, Kegulus; /?, Denebola; y, Algeiba; 8, Zosma. 

Double Stars. (1) y, Mags. 2, 3.5; Pos. 116°; Dist. 3".4; binary; 
period about 400 years. (2) t, Mags. 4 and 7; Pos. 65°; Dist. 2". 5; 
yellow and bluish ; easily recognized by aid of the map. (3) 54, 
Mags. 4.5, 7; Pos. 103°; Dist. 6". 2. Found by producing the line 
from /J through 8 half its length. 

37. Leo Minor and Sextans (Map III.). — Leo Minor is an 
insignificant modern constellation composed of a few small stars north 
of Leo, between it and the hind feet of Ursa Major. It contains 
nothing deserving special not ; ce. A similar remark holds as to Sex- 
tans even more emphatically. 

38. Hydra (Map III.). — This constellation, with its riders 
Crater and Corvus, is a large and important one, though not 
very brilliant. The head is marked by a group of five or six 
fourth and fifth magnitude stars just 15° south of Prsesepe. 
A curving line of small stars leads down southeast to a, " Cor 
Hydrae" a small second or bright third magnitude star stand- 

492 



§ 38] VIRGO. 27 

ing very much alone. From there, as the map shows, an 
irregular line of fourth-magnitude stars running far south and 
then east, almost to the boundary of Scorpio, marks the crea- 
ture's body and tail, the whole covering almost six hours of 
right ascension, and very nearly 90° of the sky. About the 
middle of his length, and just below the hind feet of Leo (30° 
due south from Denebola), we find the little constellation of 
Crater ; and just east of it the still smaller but much more 
conspicuous one of Corvus, with two second-magnitude stars 
in it, and four of the third and fourth magnitudes. It is well 
marked by a characteristic quadrilateral (see map), with 8 and 
rj together at its northeast corner. The order of the letters 
differs widely from that of brightness in this constellation, 
suggesting that changes may have occurred. 

Names, a Hydne, Alphard or Cor Hydrce ; a Crateris, A Ikes ; 
a Corvi, Alchiba ; 8 Corvi, Algores. 

Double Stars. (1) € Hydrae (the northernmost one of the group 
that marks the head), Mags. 4, 8; Pos. 220°; Dist. 3".5 ; yellow and 
purple. (2) 8 Corvi, Mags. 3, 8; Pos. 210 c ; Dist. 24"; yellow 
and purple. (3) Nebula, # IV. 27, A.R. 10 h 19 m ; Dec. S. 18° 2' (3° 
S. and J°W. of /x — see map). Bright planetary nebula, about as 
large as Jupiter. 

39. Virgo (Map III.). — East and south of Leo lies Virgo, 
the seventh zodiacal constellation, bounded on the north by 
Bootes and Coma Berenicis, on the east by Bootes and Libra, 
and on the south by Corvus and Hydra. Its a, Spica Vir- 
ginis, is of the 1± magnitude and, standing rather alone 10° 
south of the celestial equator, is easily recognized as the 
southern apex of a nearly equilateral triangle which it forms 
with Denebola (/? Leonis) to the northwest, and Arcttirus 
northeast of it. /? Virginis of the third magnitude is 14° due 
south of Denebola. A line drawn eastward and a little south 
from /? (third magnitude) and then carried on, curving north- 
ward, passes successively (see map) through rj, y, 8, and e, 

493 



28 URANOGRAPHY. [§ 39 

of the third magnitude (notice the word formed by the letters 
Begde, like Bagclei in Cassiopeia, Art. 9). lies nearly mid- 
way between a and 8. There are also a number of other fourth- 
magnitude stars. 

Names, a, Spica and Azimecli ; /3, Zavljava; e, Vindemiatrlx. 

Double Stars. (1) y, (Binary; period 185 years; not quite half-way 
from Spica to Denebola, and a little west of the line), Mags. 3, 3; Pos. 
(1890) 330°; Dist. 5".5 ; very easy and fine (Astr. Fig. 113). (2) 6 
(two-fifths of the way from Spica towards S), Triple; Mags. A 4.5, 
B 9, C 10; Pos. A-B, 345°, Dist. 7"; A-C, Pos. 295°, Dist. 65". 
(3) o (one-third of the way from Denebola towards y Virginia), 
Mags. 6 and 8 ; Pos. 228° ; Dist. 3".5. Spica is a spectroscopic 
binary (Art. 465*). 

Nebulce. (1) M. 49 ; A.R. 12 h 24 m ; Dec. + 8° 40'. Forms an equi- 
lateral triangle with 8 and e. It lies in the remarkable " nebulous " 
region of Virgo. But most of the nebulae are faint, and observable 
only with large telescopes. (2) # IT. 74 and 75; A.R. 12 h 47 m ; Dec. 
+ 11° 53' ; two in one field, 2° west and a little north of e. (3) M. 86 
(midway between Denebola and e) ; A.R. 12 h 20 m ; Dec. -f 13° 36 . A 
large telescope shows nearly a dozen nebulae within 2° of this place. 

40. Coma Berenicis (Map III.). — This little constellation, com- 
posed of a great number of fifth and sixth magnitude stars, lies 30° 
north of y and -q Virginis, and about 15° northeast of Denebola. It 
contains a number of interesting double stars, but they are not easily 
found without the help of an equatorial mounting and graduated 
circles. 

41. Canes Venatici (The Hunting Dogs). — These are the 
dogs with which Bootes is pursuing the Great Bear around the 
pole : the northern of the two is Asterion, the southern Oliara. 
Most of the stars are small, but a is of the 2\ magnitude, and 
is easily found by drawing from rj Ursae Majoris (the star in 
the end of the Dipper-handle) a line to the southwest, perpen- 
dicular to the line from rj to £ (Mizar) and about 15° long : it 
is about one-third of the way from rj Ursse Majoris to 8 Leonis. 
With Arcturus and Denebola it forms a triangle much like 
that which they form with Spica. 

494 



§ 41] BOOTES. 29 

Names, a is known as Cor Caroli (Charles IT. of England). 

Donhle Stars. (1) a, or 12 Canuin, Mags. 3 and 5; Pos. 227°; Dist. 
20". (2) 2 Canum (one-third of the way from a towards 8 Leonis), 
Mags. 6 and 8; % Pos. 260°; Dist. 41".3; orange, smalt blue. 

Nebulae. (1) M. 51 ; A.E. 13 h 25™ ; Dec. 47° 49' (3° west and some- 
what south of Benetnasch). A faint double nebula in small tele- 
scopes ; in great ones, the wonderful " Whirlpool Nebula " of Lord 
Rosse. (2 ) M. 3 ; bright cluster (half a degree north of the line from 
a Canum to Arcturus, and a little nearer the latter). It is one of 
the variable-star clusters discovered in 1895 (see Art. 555*). 

42. Bootes (Maps III. and I.). — This fine constellation is 
bounded on the west by Ursa Major, Canes Venatici, Coma 
Berenicis, and Virgo, and on the south by Virgo. It extends 
more than 60° in declination, from near the equator quite to 
Draco, where the uplifted hand overlaps the tail of the Bear. 
Its principal star, Arcturus, is of a ruddy hue, and in bright- 
ness is excelled only by Sirius among the stars visible in our 
latitudes. Canopus and a Centauri are reckoned brighter, but 
they are southern circumpolars. Arcturus is at once recog- 
nized by its forming with Spica and Denebola the great tri- 
angle already mentioned (Art. 39). Six degrees west and a 
little south of it is 77, of the third magnitude, w r hich forms 
with it, in connection with v, a configuration like that in the 
head of Aries, e is about 10° northeast of Arcturus, and in 
the same direction about 10° farther lies 8. A pentagon is 
formed by these two stars along with /?, y, and p. " Bootes " 
means " the shouter " (or, according to others, " the herds- 
man "). 

Names, a, Arcturus; /3, Nekkar; e, Izar ; rj, Muphrid ; y, 
Seginus. 

Double Stars. (1) e, Mags. 3, 6; Pos. 325°; Dist. 3".l; orange and 
greenish blue ; very fine. (2) £ (about 9° southeast from Arcturus, 
at right angles to the line ae), Mags. 3.5, 4; Pos. 295°; Dist. 0".S; 
a good test for a 4-inch glass. (3) tt (2J° north of £), Mags. 4.9, 6 ; 
Pos. 101°; Dist. 5".3. (4) £ (10° due east from Arcturus, 3° N.E. 
from tt), Mags. 4.7, 6.6 ; Pos. (1890) 264° ; Dist. 4" ; yellow and purple. 
Binary; period 127 years. 

495 



30 TIHANOGRAPHY. [§ 43 

43. Corona Borealis (Map III.). — This beautiful little con- 
stellation lies 20° northeast of Arcturus, and is at once rec- 
ognizable as an almost perfect semicircle composed of half a 
dozen stars, among which the brightest, a, is of the second 
magnitude. The extreme northern one is 0; next comes /}, 
and the rest follow in the j3 a y 8 e i (Bagdei) order, just as 
in Cassiopeia. 

Names, a, Gemma, or Alphacca. 

Double Stars. (1) £ (nearly pointed at by e-8 Bootis ; 7° from e), 
Mags. 5, G; Pos. 301°; Dist. G"; white and greenish. (2) rj, rapid 
binary, at certain times can be split by a 4-inch glass. Mags. 6, G.5; 
pointed at by the line from a through /?, 2° beyond f3. The tempo- 
rary star of 1866 (Astr. 450) lies U° S.E. of e Coronse. 

44. Libra (Map III.). — This is the eighth of the zodiacal 
constellations, and lies east of Virgo, bounded on the south by 
Centaurus and Lupus, on the east by the upstretched claw of 
Scorpio, and on the north by Serpens and Virgo. It is incon- 
spicuous, the most characteristic figure being the trapezoid 
formed by the lines joining the four stars a, t, y, /?. /?, which 
is the northernmost of the four, is the brightest (2± magni- 
tude), and is about 30° nearly due east from Spica, while a is 
about 10° southwest of /?. The remarkable variable 8 Librae 
is 4° west and a little north from /?. Most of the time it is 
of the 4^ or fifth magnitude, but runs down nearly two magni- 
tudes at the minimum. 

Names, a, Zuben el Genuhi ; (3, Zuben el Chamall. 

Cluster. M. 5; All. 15'» 12'"; Dec. N. 2° 32'. This is within tl 
boundaries of Serpens, and just a little north and west of the fifth- 
magnitude star 5 Serpentis. It is a variable-star cluster (Art. 555*). 

45. Antlia, Centaurus, and Lupus (Map III.)- — These constel- 
lations lie south of Hydra and Libra. Antlia Pneumatica (the " Air- 
Pump ") is a modern constellation of no importance and hardly recog- 
nizable by the eye, having only a single star as brio-ht as the 4} mag- 

496 



le 



§ 45] SCORPIO. 31 

nitude. Centaurus, on the other hand, is an ancient and extensive 
asterism, containing in its (south) circumpolar portion two stars of 
the first magnitude : a Centauri stands next after Sirius and Canopus 
in brightness, and, as far as present knowledge indicates, is our nearest 
neighbor among the stars. The part of the constellation which be- 
comes visible in our latitudes is not specially brilliant, though it con- 
tains several stars of the 2 J and third magnitude in the region that 
lies south of Corvus and Spica Virginis. A line from c Virginis 
through Spica, produced a little more than its own length, will strike 
very near 6, a solitary star of the 2 J magnitude in the Centaur's 
left shoulder, l (third mag.) lies 11° west of 8, and rj (third mag.) 
9° southeast ; while 5° or 6° south of the line from 6 to l lies a tangle 
of third-magnitude stars, which, if they were at a higher elevation, 
would be conspicuous. Centaurus is best seen in May or early in 
June. 

Lupus, also one of Ptolemy's constellations, lies due east of Cen- 
taurus and just south of Libra. It contains a considerable number of 
third and fourth magnitude stars ; but is too low for any satisfactory 
study in our own latitudes. It is best seen late in June. These 
constellations contain numerous objects interesting for a southern 
observer, but nothing available for our purpose. 

46. Scorpio (or Scorpius) (Map IV.). — This, the ninth of 
the zodiacal constellations, and the most brilliant of them, 
lies southeast of Libra, which in ancient times used to form 
its claws (Chelae). It is bounded north by Ophiuchus, south 
by Lupus, Norma, and Ara, and east by Sagittarius. It is 
recognizable at once on a summer evening by the peculiar con- 
figuration, like a boy's kite, with a long streaming tail reach- 
ing far down to the southern horizon. Its principal star, 
Antares, is of the first magnitude and fiery red, like the 
planet Mars. From this it gets its name, which means "the 
rival of Ares" (Mars). (3 (second magnitude) is in the arch 
of the kite bow, about 8° or 9° northwest of Antares, while 
the star which Bayer lettered as y Scorpii is well within Libra, 
20° west of Antares. (There is no little discordance and con- 
fusion among Uranographers as to the boundary between the 

497 



32 TJRANOGRAPHY. [§ 46 

two constellations.) The other principal stars of the constel- 
lation are easily found on the map ; S is 3° southwest of /3, 
while e, £, rj, 0, i, k, and A follow along in order in the tail of 
the creature, except that between e and £ is interposed the 
double ix. e, 0, and A are all of the second magnitude, and the 
others of the third. 

47. Names, a, Antares ; /?, Akrab. 

Double Stars. (1) a, Mags. 1 and 7 ; Pos. 270° ; Dist. 3. "5 ; fiery red 
and vivid green. A beautiful object when the state of the air allows 
it to be well seen. (2) /3, Triple; Mags. A 2, B 4, C 10; A-B, Pos. 
25°, Dist. 13"; A-C, Pos. 89°, Dist. 0".9. (3) v (2° due east of 0), 
Quadruple; Mags. A 4, B 5, C 7, D8; A-B, Pos. 7°, Dist. 0".8 ; 
A-C, Pos. 337°, Dist. 41";. C-D, Pos. 47°, Dist. 2".4. A beautiful 
object. (4) £ Scorpii (8J° due north from /?), Triple; Mags. A 5, 
B 5.2, C 7.5 ; A-B, (Binary) Pos. 200°, Dist. 1".4 ; £(A + B) to C, 
Pos. 65°, Dist. 7 // .3. fx 1 is a spectroscopic binary (Art. 465*). 

Clusters. (1) M. 80, A.B. 16 h 10 m ; Dec. S. 22° 42'; half-way 
between a and /?; one of the finest clusters known. (2) M. 4, A.R. 
16 h 16 m ; Dec. S. 26° 14' ; 1J° west of a; not so fine as the preceding. 

Norma lies west of Scorpio, between it and Lupus, while Ara lies 
due south of 77 and 0. Both are small and of little importance, at 
least to observers in our latitudes. 

48. Ophiuchus (or Serpentarius) and Serpens (Map IV.). — 
Ophiuchus means the "serpent-holder." The giant is repre- 
sented as standing with his feet on Scorpio, and grasping the 
" serpent/' the head of which is just south of Corona Borealis, 
while the tail extends nearly to Aquila. The two constella- 
tions therefore are best treated together. The head of Serpens 
is marked by a group of small stars 20° due east of Arcturus, 
and 10° south of Corona. /3 and y are the two brightest stars 
in the group, their magnitudes three and a half and four. 
8 lies 6° southwest of (3, and there the serpent's body bends 
southeast through a and c Serpentis (see map) to 8 and e Ophi- 
uchi in the giant's hand. The line of these five stars carried 
Upwarr 1 " ™.sses ~ V through e Bootis, and downwards 



§ 48] OPHIUCHTJS. 33 

through £ Ophiuchi. A line crossing this at right angles, 
nearly midway between € Serpentis and 8 Ophmchi, passes 
through fji Serpentis on the southwest, and \ Ophiuchi to the 
northeast. The lozenge-shaped figure formed by the lines 
drawn from a Serpentis and £ Ophiuchi to the two stars last 
mentioned forms one of the most characteristic configurations 
of the summer sky. 

a Ophiuchi (2\ magnitude) is easily recognized in connection 
with a Herculis, since they stand rather isolated, about 6° 
apart, on the line drawn from Arcturus through the head of 
Serpens, and produced as far again, a Ophiuchi is the eastern 
and the brighter of the two. It forms with Vega and Altair a 
nearly equilateral triangle. /3 Ophiuchi lies about 9° southeast 
of a ; and 5° east and a little south of /3 are five small stars 
in the Milky Way, forming a V with the point to the south, 
much like the Hyades of Taurus. They form the head of the 
now discredited constellation " Poniatowski's Bull" {Taurus 
Poniatovii), proposed in 1777. 

49. Names, a Ophiuchi, Ras Alaghue ; /?, Cebalrai ; 8, Yed ; X, 
Marjic: a Serpentis, Unukalhai ; 6, Alya. 

Double Stars. (1) X Ophiuchi, Binary ; period, 234 years ; Mags. 4, 
6 ; Pos. (1890) 42° ; Dist. 1".6. (2) 70 Ophmchi (the middle star in 
the eastern leg of the V of Poniatowski's Bull), Binary ; period, 93 
years ; Mags. 4.5, 7 ; Pos. (1890) 340° ; Dist. 2". The position angle 
changes very rapidly just now, and the star is too close to be resolved 
by a small instrument. (3) 8 Serpentis, Mags. 4, 5 ; Pos. 185° ; Dist. 
3".6 ; very pretty. (4) Serpentis, Mags. 4, 4.5; Pos. 104°; Dist. 21". 
(5) v Serpentis (4° N.E. of rj Ophiuchi), Mags. 4.5, 9 ; Pos. 31° ; Dist. 
51" ; sea-green and lilac. 

Clusters. (1) M. 23, A.R. 17* 50 m ; Dec. S. 19° 0'. Fine low- 
power field. (2) M. 12, A.R. 16 h 41 m ; Dec. S. 1° 45'. On the line 
between j3 and e Ophiuchi, one-third of the way from e. (3) M. 10, 
A.R. 16 h 51 m ; Dec. S. 3° 56'. On the line between /3 and £ Ophiuchi, 
two-fifths of the way from £. (4) 9 VIII. 72, A.R. 18* 22 m ; Dec. N. 
6° 29'. Pointed at by the eastern leg of the Poniatowski V. 8° from 
70 Ophiuchi, 

499 



34 UKANOGRAPHY. [§ 50 

50. Kercules (Maps I. and IV.). — This noble constellation 
lies next north of Ophiuchus, and is bounded on the west by 
Serpens, Corona, and Bootes, while to the east lie Aquila, Lyra, 
and Cygnus. On the north is Draco. The hero is represented 
as resting on one knee, with his foot on the head of Draco, 
while his head is close to that of Ophiuchus. The constella- 
tion contains no stars of the first or even of the second mag- 
nitude, but a number of the third. The most characteristic 
figure is the keystone-shaped quadrilateral formed by the stars 
€, £, rj, with 7r and p together at the northeast corner. It lies 
about midway on the line from Vega to Corona. The line ?re, 
carried on 11°, brings us to /?, the brightest star of the aster- 
ism ; and y and k lie a few degrees farther along on the same 
line continued toward y Serpentis. The angle e/3a is a right 
angle opening towards Lyra, a is irregularly variable, besides 
being double. 

51. Names, a, Ras Algethi ; f3, Korneforos. 

Double Stars. (1) a, Mags. 3, 6 ; Pos. 119°; Dist. 4".5 ; orange and 
blue. A very beautiful object for a 4-inch glass (Astr. Fig. 113). (2) £ 
(the S.W. corner of the "Keystone"), Binary; period, 34 y. (Astr. Fig. 
113) ; Mags. 3, 6.5 ; Pos. (1890) 66° ; Dist. 1".5. Rather difficult for a 
small instrument. (3) p (2J° east of it at the N.W. corner of the 
" Keystone "), Mags. 4, 5 ; Pos. 312° ; Dist. 4" ; white, emerald green. 
(4) 8 (on the line from rj through € produced nearly its own length), 
Mags. 3, 8; Pos. 184°; Dist. 18"; white, light blue. Apparently an 
" optical pair " ; the relative motion being rectilinear. (5) /x (nearly 
midway between Vega and a Herculis — see map), Triple', Mags. A 4, 
.5, C 10; A, B + C , Pos. 246°; Dist. 31". B-C, too faint and close 

for separation by any but large telescopes; Dist. about 1"; position 
angle rapidly changing — about 20° in 1890. (6) 95 Herculis (the 
N.W. corner of a little quadrilateral [sides 1° to 2°] of fourth and 
fifth mag. stars, on line from p through /x, produced two-thirds its 
length), Mags. 5.5 and 6; Pos. 262°; Dist. 6''; light green, cherry-red. 
Peculiar in showing contrast of color between nearly equal components. 
Clusters. (1) M. 13, A.R. 16 h 37 ra ; Dec. 36° 41'. Exactly on the 
western boundary of the Keystone, one-third the way from rj towards 

500 



§ 51] LYRA. 35 

£. On the whole, the finest of all star clusters. (2) M. 92, A.R. 
17 h 13 m ; Dec. 43° 16' (6° north and a little west of p). Fine, but not 
equal to the other. 

52. Lyra (Map IV.). — The great white or blue star Vega 
sufficiently marks this constellation. It is attended on the 
east by two fourth-magnitude stars, e and £, which form with 
it a little equilateral triangle having sides about 2° long. /} 
and y of the third magnitude (/3 is variable) lie about 8° 
southeast from Vega, 2-|° apart. 

Double Stars. (1) Vega itself has a small companion, 11th mag. ; 
Pos. 160°; Dist. 48". Only optically connected ; the small star does 
not share the proper motion of the larger one, and has been used as a 
reference point in measuring Vega's parallax. (2) /?, multiple; i.e., 
it has three small stars near it, forming a very pretty object with a 
low power. (3) e 1 and e 2 , Quadruple (the northern of the two which 
form the little triangle with a.) A sharp eye unaided by a telescope 
splits the star, and a small telescope divides both the components 
(see Astr. 468, and Fig. 113): e x (or 4 Lyras), Mags. 6, 7; Pos. 12°; 
Dist. 3".2. e 2 (or 5 Lyrse), Mags. 5.5, 6 ; Pos. 132° ; Dist. 2".5. e, e 2 , 
Pos. 173° ; Dist. 207". On the whole, the finest object of the kind. 
(4) £, Mags, 4, 6; Pos. 150°; Dist. 44". (5) v (10° E. of Vega), 
Mags. 4:5, 8; Pos. 85°; Dist. 28"; yellow, indigo. (6) 8; fine field 
for low powers. 

Nebula. M. 57, the Annular Nebula. A.R. 18 h 49 m ; Dec. 32° 53'. 
Between (3 and y, one-third of the way from /?. (Art. 471.) 

53. Cygnus (Maps I. and IV.). — This lies due east from 
Lyra, and is easily recognized by the cross that marks it. The 
bright star a (1^- magnitude) is at the top, and (3 (third mag- 
nitude) at the bottom, while y is where the cross-bar from S to 
€ intersects the main piece, which lies along the Milky Way 
from the northeast to the southwest. £ is (nearly) on the pro- 
longation of the line from y through e, not quite so far from 
c as e from y. 

Names, a, Arided, or Deneb Cygni (there are other Denebs ; e.g., 
Deneb Kaitos in Cetus) ; /?, Albireo; y, Sadr. 

501 



36 URANOGRAPHY. [§ 53 

Double Stars. (1) ft, Mags. 3.5, 7; Pos. 56°; Dist. 35"; orange, 
smalt blue. This is the finest of the colored pairs for a small tele- 
scope. (2) fM (as far beyond £ as £ is east of e, at the tip of the east- 
ern wing), Mags. 5 and 6 ; Pos. 118°; Dist. 3". 8. (3) x (one-third of 
the way from ft towards y), Mags. 5 and 9 ; Pos. 73°; Dist. 26"; yel- 
low and blue. (4) 61 Cygni (easily found by completing the parallel- 
ogram of which a, y, and e are the other three corners, cr and r form 
a little triangle with 61, which is the faintest of the three), Mags. 
5.5, 6 ; Pos. (1890) 121°; Dist. 20". This is the star of which Bessel 
measured the parallax in 1838 (Astr. 521), — apparently our second 
nearest neighbor. 

8 is also a fine double, but too difficult for an instrument of less 
than six inches' aperture. 

Clusters. (1) M. 39, A.K. 21 h 28 m ; Dec. 47° 54' (about 3° north of p ; 
p itself (fourth mag.) being found by drawing a line from 8 through 
a, and carrying it an equal distance beyond. (2) # VIII. 56, A.R. 
20 h 19 m ; Dec. 40° 20'. Beautiful group, J° north and a little east of 
y. The bright spots in the Milky Way all through Cygnus afford 
beautiful fields for a low power. 

54. Vulpecula et Anser (Map IV.). — This little constella- 
tion is one of those originated by Hevelius, and has obtained 
more general recognition among astronomers than most of his 
creations. It lies just south of Cygnus, and is bounded to the 
south by Delphinus, Sagitta and Aquila. 

It has no conspicuous stars, but contains one very interesting tele- 
scopic object, — the "Dumb-Bell Nebula," — M. 27, A.R. 19 h 54 m : 
Dec. 22° 23'. On a line from y Lyrse through ft Cygni, produced as far 
again, where this line intersects another drawn from a Aquilse through 
y Sagittse, 3J° north and half a degree east of the latter star. 

55. Sagitta (Map IV.). — This little asterism, though very incon- 
spicuous, is one of the old 48. It lies south of Vulpecula, and the two 
stars a and ft, which mark the feather of the arrow, lie nearly midway 
between ft Cygni and Altair, while its point is marked by y, 5° farther 
east and north. 

Double Stars. (1) £ (|° N.W. of 8, the middle star in the shaft of 
the arrow), Mags. 5.5, 9; Pos. 312°; Dist. 8".6: the larger star is itself 
close double, distance about \", making an interesting triple system. 

502 






§ 56] AQUILA. 37 

56. Aquila (Map IV.). — This constellation lies on the ce- 
lestial equator, east of Ophiiichus and north of Sagittarius 
and Capricornus. It is bounded on the east by Aquarius and 
Delphinus, and on the north by Sagitta. Its characteristic 
configuration is that formed by Altair (the standard first-mag- 
nitude star), with y to the north and f3 to the south. It lies 
about 20° south of ft Cygni, and forms a fine triangle with 
Vega and a Ophiuchi. 

Double Star. (1) ?r Aquilse (1J° N.E. of y), Mags. 6 and 7; Pos. 
120°; Dist. 1".5. Good test for 3J-inch glass. 

Cluster. M. 11, A.R. 18 h 45 m ; Dec. S. 6° 24'. A fine fan-shaped 
group of stars in the Milky Way. A line carried from Altair through 
S Aquilse (see map), and prolonged once and a half as far again, will 
find it about 4° S.W. of A. 

The southern part of the region allotted to Aquila on our maps has 
been assigned to Antinous. This constellation was recognized by some 
even in Ptolemy's time ; but he declined to adopt it. Hevelius appro- 
priated the eastern portion of " Antinous " for his constellation of 
w Scutum Sobieski" and M. 11 falls just within its limits. 

57. Sagittarius (Map IV.). — This, the tenth of the zodia- 
cal constellations, is bounded north by Aquila and Ophiuchus, 
west by Scorpio and Ophiuchus (though Bode and some other 
authorities crowd in a piece of " Telescopium " between it and 
Scorpio), south by Corona Australis, Telescopium, and Indus, 
and east by Microscopium and Capricornus. It contains no 
stars of the first magnitude, but a number of the 2\ and third. 

The most characteristic configuration is the little inverted 
u milk dipper " formed by the five stars, A, <f>, o-, r, and £, of 
which the last four form the bowl, while X (in the Milky Way) 
is the handle. §, y, and e, which form a triangle right-angled 
at 8, lie south and a little west of A, the whole eight together 
forming a very striking group. There is a curious disregard 
of any apparent principle in the lettering of the stars of this 
constellation; a and /? are stars not exceeding in brightness 

503 



38 TJRANOGRAPHY. [§ 57 

the fourth magnitude, about 4° apart on a north and south 
line and lying some 15° south and 5° east of £ (see map). 
The Milky Way in Sagittarius is very bright, and complicated 
in structure, full of knots and streamers, and dark pockets. 

Names. X, Kaus Borealis ; S, Kaus Media; c, Kaus Australis ; cr, 
Sddira. This star is strongly suspected of irregular variability. 

Double Stars. (1) fx 1 (7° KW. of A ; on the line from £ through cf> 
produced), Triple; Mags. A 3.5, B 9.5, C 10; A-B, Pos. 315°, Dist. 
40"; A-C, Pos. 114°, Dist. 45". 

Clusters and Nebulce. (1) M. 22, A.R. 18 h 29 m ; Dec. S. 24° 0' (3° 
X.W. of X, and midway between /x and o-). Capital object for a 4-inch 
telescope. (2) M. 25, A.R. 18 h 25 m ; Dec. S. 19° 10' (7° north and 1° 
east of X; visible to naked eye). (3) M. 8; A.R. 17 h 57 m ; Dec. S. 
24° 21' (a little south of the line cf>X produced, and as far from X as 
X from <£; also visible to naked eye). (4) # IV. 41, The Trifid 
Nebula, A.R. 17 h 55 m ; Dec. S. 23° 2' (1}° north of M. 8, and almost 
exactly on the line <f>X produced). A very beautiful and interesting 
object. 

58. Capricornus (Map IV.). — This, the eleventh of the 
zodiacal constellations, follows Sagittarius on the east. It has 
Aquarius and Aquila (Antinous) on the north, Microscopium 
and Piscis Austrinus on the south, and Aquarius on the east. 
It has no bright stars, but the configuration formed by the 
two a's (a x and a 2 ) with each other and with /?, 3° south, is 
characteristic and not easily mistaken for anything else. The 
two a's, a pretty " double " to the naked eye, lie on the line 
from (3 Cygni (at the foot of the cross) through Altair, pro- 
duced about 25°. On the line a/3, about 3° distant, lies p (of 
the fourth magnitude), with two other small stars near it. 
From this a line 20° long, carried due east through and i (of the 
fourth magnitude), brings the eye to y and S of the third, the 
latter marking the constellation's eastern limit. 

Names, a, Algiedi (prima and secundd) ; 8, Deneb Algiedi. 
Double Stars. (1) a x and a 2 (pretty with a very low power), Mags. 
3 and 4; Dist. 6 ; 13". cu* has also a very faint companion, invisible 

504 



§ 58] DELPHINUS. 39 

with any telescope of less than 6-inch aperture ; Pos. 150°; Dist. 7". 5. 
The companion is itself double; Dist. about 1"; Pos. 240°. (2) /?, 
Mags. 3.5, 7 ; Pos. 267° ; Dist. 3' 25", The companion is also a close 
and difficult double. (3) p (the northern star in the little triangle it 
forms with tt and o), Mags. 5, 9 ; Pos. 177°; Dist. 3". 8. (4) tt (the 
S.W. one in the same triangle), Mags. 5, 9 ; Pos. 146°; Dist. £".5. 

Nebula. M. 30, A.R. 21 h 34 m ; Dec. S. 23° 42' (about 1° west and 
a little north of 41 Capricorni, a fifth-magnitude star, 7° south of y 
Capricorni) . 

59. Delphinus (Map IV.). — This little asterism is ancient, 
and unmistakably characterized by the rhombus of third-mag- 
nitude stars known as " Job's Coffin." It lies about 15° north- 
east of Altair, bounded north by Vulpecula and west by Aquila. 
There are a few stars visible to the naked eye in addition to 
the four that form the rhombus. Epsilon, about 3° southwest, 
is the only conspicuous one. 

Names, a, Svalocin ; /3, Rotanev. These were given in joke by 
Xicolaus Cacciatore, a Sicilian astronomer, about 1800. The letters 
of the two names reversed make Nicolavs Venator ; Venator being the 
translation of the Italian " Cacciatore," which means "Hunter." The 
joke is good enough to keep. 

Double Stars. (1) y (at the N.W. angle of the rhombus), Mags. 4, 
7; Pos. 271°; Dist. 11".3. (2) /?, a very close and rapid binary, 
beyond the reach of all but large telescopes. It has, however, two 
little companions, distant about 30". 

60. Equuleus (Map IV.). — This little constellation is still 
smaller than the Dolphin, and contains no such characteristic star 
group. It lies about 20° due east of Altair, and 10° S.E. of Delphinus 
(see map). 

Double Stars. (1) e, Mags. 5, 7.5 ; Pos. 73°; Dist. 11". The larger 
star is also close double ; Mags. 5.5. and 7 ; Pos. 290° ; Dist. 0".9. Per- 
haps resolvable with a 4-inch telescope. 

61 . Lacerta (Maps I. and IV. ) . — This is one of Hevelius's mod- 
ern constellations, lying between Cygnus and Andromeda, with no 
stars above the 4 h magnitude. It contains a few telescopic objects, 
but nothing suited to our purpose. 

505 



40 UKANOGRAPHY. [§ 62 

62. P6g£sus (not Pegas'us) (Map IV.). — This covers an 
immense space which, is bounded on the north by Andromeda 
and Lacerta, on the west by Cygnus, Vulpecula, Delphinus, 
and Equuleus, on the south by Aquarius and Pisces, and on 
the east by Pisces and Andromeda. Its most notable config- 
uration is " the great square," formed by the second-magnitude 
stars a, /?, and y Pegasi, in connection with a Andromeda 
(sometimes lettered 8 Pegasi) at its northeast corner. The 
stars of the square lie in the body of the horse, which has no 
hindquarters. The line drawn from a Andromedse through 
a Pegasi, and produced about an equal distance, passes through 
£ and £ in the animal's neck, and reaches (third magnitude) 
in his ear. Epsilon, 8° northwest of 0, marks his nose. The 
forelegs are in the northwestern part of the constellation just 
east of Cygnus, and are marked, one of them by the stars rj 
and 7r, the other by i and k. 

Names, a, Markab ; (3, S cheat ; y, Algenib : e, En if. 

Double Star, k, Mags. 4, 11 ; Pos. 302° ; Dist. 12". The large star 
is also itself an extremely close double; Dist. 0".3 ; (pointed at by 
the northern edge of the " square," at a distance one and a quarter 
times its length.) 

Cluster. M. 15, A.R. 21* 24 m ; Dec. 11° 38' (on the line from 8 
through e, produced half its length, and just west of a sixth-magni- 
tude star). 

63. Aquarius (Map IV.). — This, the twelfth and last of 
the zodiacal constellations, extends more than 3^- hours in 
right ascension, covering a considerable region which by 
rights ought to belong to Capricornus. It is bounded north 
by Delphinus, Equuleus, Pegasus, and Pisces ; west by Aquila 
and Capricornus ; south by Capricornus and Piscis Austrinus. 
and east by Cetus. The most notable configuration is the 
little Y of third and fourth magnitude stars which marks the 
" water jar" from which Aquarius pours the stream that 
meanders down to the southeast and south for 30°, till it 

500 



§ 63] PISCIS ACJSTRINUS. 41 

reaches the Southern Fish. The middle of the Y is about 18° 
south and west of a Pegasi, aud lies almost exactly on the 
celestial equator. A line drawn west and a little south from 
y (the westernmost star of the Y) to a Capricorni, passes 
through /? (third magnitude) at one-third of the way, and 
through fji and e (fourth and 3J) two-thirds of the way. a 
(third magnitude) lies 4° west and a little north of y. 8 (third 
magnitude) lies about half-way between the Y and Fomalhaut 
in the Southern Fish, 3° or 4° east of the line that joins them. 

Names, a, Saad el Melik ; (3, Saad el Sund ; 8, Skat. 

Double Stars. (1) £ (the central star of the Y), Mags. 4, 4.5; Pos. 
332° ; Dist. 3".6 ; pretty and easy. (2) 12 Aquarii (7° due west of /3, 
and the brightest star in the vicinity), Mags. 5.5/8.5; Pos. 190°; Dist. 
2". 8 ; yellowish white and light blue. 

Clusters and Nebulce. (1) M. 2; A.R. 21 h 17 m ; Dec. S. 1° 22' (on 
the line drawn from £ through a, produced one and a quarter times its 
own length). (2) # IV. 1, A.R. 20 h 58 m ; Dec. S. 11° 50' (nearly on 
the line from a through (3, produced its own length, and 1J C w x est of 
v ; fifth magnitude) ; planetary nebula, bright and vividly green. 

64. Piscis Austrmus (or Australis) (Map IV.). — This small 
constellation, lying south of Aquarius and Capricornus, pre- 
sents little of interest. It has one bright star, Fomalhaut 
(pronounced Fomalo)', of the 1\ magnitude, which is easily 
recognized from its being nearly on the same hour-circle with 
the western edge of the great square of Pegasus, 45° to the 
south of a, and solitary, having no star exceeding the fourth 
magnitude within 15° or 20°. It contains no telescopic objects 
available for our purpose c 

South of it, barely rising above the southern horizon, lie the con- 
stellations of Microscopium and Grus. The former is of no account. 
The latter is a conspicuous constellation in the southern hemisphere, 
and its two brightest stars, a and (3, of the second magnitude, rise 
high enough to be seen in latitudes south of Washington. They lie 
about 20° south and west of Fomalhaut. 

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ASTRONOnY 



By Charles A. Young, Ph.D., LL.D., Professor of Astronomy in 
Princeton University, Princeton, N.J., and author of The Sun. 

A Series of text-books on astronomy for high schools, academies, and colleges. 

Prepared by one of the most distinguished astronomers of the world, 

a most popular lecturer, and a most successful teacher. 

Lessons in Astronomy. Including Uranography. Revised Edition. 
i2mo. Cloth. Illustrated. 366 pages, exclusive of four double-page 
star maps. For introduction, $1.20. 

Elements of Astronomy. With a Uranography. i2mo. Half leather, 

472 pages, and four star maps. For introduction, $1.40. 

Uranography. From the Elements of Astronomy. Flexible covers. 42 pages, 
besides four star maps. For introduction, 30 cents. 

General Astronomy. A text-book for colleges and technical schools. 
8vo. 551 pages. Half morocco. Illustrated with over 250 cuts and 
diagrams, and supplemented with the necessary tables. For intro- 
duction, $2.25. 

The Lessons in Astronomy (recently brought up to date) was 
prepared for schools that desire a brief course free from 
mathematics. Everything has been carefully worked over 
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pains has been taken not to sacrifice accuracy and truth 
to brevity, and no less to bring everything thoroughly up 
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The Elements of Astronomy is an independent work, and 
not an abridgment of the author's General Astronomy. It 
is a text-book for advanced high schools, seminaries, and 
brief courses in colleges generally. Special attention has 
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far as they go. 

The eminence of Professor Young as an original investi- 
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and an instructor in college classes, led the publishers to 
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It is conceded to be the best astronomical text-book of its 
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Experimental Physics 



WILLIAM ABBOTT STONE, 

Instructor in Physics in the Phillips Exeter Academy, 



l2mo. Cloth. 378 pages. Illustrated. For introduction, $1.00. 



'TT'HIS book is the result of an experience of nearly ten 
^ years in teaching Experimental Physics to classes con- 
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It is intended for use in the upper classes in High Schools 
and Academies, and for elementary work in Colleges. It 
consists of a carefully arranged and thoroughly tested series 
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The general results of the experiments are enforced by 
numerous examples, many of which have been drawn from 
Harvard Examination Papers. 






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